I lost my first p/c because of trojans about a couple of years ago and when I bought the new one I started from the very first moment to suffer the same way. In the first system I did not use antivirus or firewall the first years I surfed, about 1998 that is, as then the security programs weren't so well known. I used Norton Internet antivirus and Zone Alarm firewall as they were the best to me around 2000-2005.
In November 2005 I had the total blackout of my system, luckily I had saved my data in a memory stick.
I bought another system with Windows XP and I had immediately blackout with and because of Norton alerts, I restored it to the purchase date and installed Nod32 and ZAP and continued to exist, but trojans did not stop to invade, I find them occasionally with Netscape antispyware check (before to be discontinued) Adaware or Spybot but others, undetected, still exist and provoke problems in my p/c.
I gave up with this struggle and just use my p/c when and the way trojans let me do it.
But now, from dial-up I must go to ADSL for money reasons and I wonder how this trojan problem could react with ADSL.
Have absolutely no idea if passing to fast internet would for instance automatically erase trojans or on the contrary if trojans in the ADSL could simply stop me from connecting permanently.
There is rather no way to clean my system for good, I'm absolutely passimist about that.
So, the question is IF I HAVE UNDETETCTED MALWARE IN MY SYSTEM AND GO TO ADSL (FAST INTERNET) HOW THIS MALWARE WILL AFFECT MY CONNECTING TO THE NET?

Hopefully you will not.

What AV are you using now and do you have it update daily?

What makes you say you do have malware?

I would download and run malwarebytes free version to see if it detects anything and help remove things it does find
Malwarebytes.org

Paid version offers:
Activating the full version unlocks realtime protection, scheduled scanning, and scheduled updating

So use it to scan manually and see what comes up

'Hopefully' is not enough.
I must have internet connection any time and with dial-up, trojans simply do not let me to connect.
When I had a stable unique internet provider they stopped me from connecting so I started using internet cards, that is prepaid cards of different providers, of several hours duration, I had always some of them available and when they stopped me from connecting with my permanent provider I used them instead.
Gradually I saw there is no use for a permanent provider under the circumstances.
But if now I pass to fast internet beside other things, I will again have a unique provider and probably the same problem as before.
How do I not know I have a trojan?
I erased a couple of weeks ago System Doctor 2006 with Spybot, and did not check manually furthermore.
How much time do you have so that I will describe my problems with my p/c?
Time and date of it are constantly changing in an absurd way that is not by some stable amount of hours each time, in order to confuse my ZAP logs so that when I send abuse notifications to hackers' providers they cannot locate them by the time of the log.
My everything's vertical bar (that is my notepad's, my word's, my browsers') is by time to time constantly moving up and down so that I cannot read or write anything at all.
I have access denials whenever hackers do not like the site I want to visit, for instance my homepage, and millions of other things.
The question I asked is NOT HOW I WILL CLEAN FROM TROJANS, BUT HOW TROJANS REACT WITH FAST INTERNET.

My answer was, hopefully it will not but try these things to see if it can be removed or prevented from hampering your "plan"

Hope you do find an answer to your question as it seems you would like to keep the malware and work around it.

"I'd like to keep it?"
I do not believe above site will help me to remove malware.
10 years of surfing, very much money to replace all hardware spoiled and broken because of trojans, millions of hours struggling against trojans when Symantec didn't even know the existence of trojans and insisted that a have a virus when all antivirus found me clean, I thought I was crazy seeing my p/c shutting down without me having ordered so, reacting crazy even when off-line, agonies, installments in credit cards which are still overloaded because I paid a new tower, a new scanner-fax-copier-printer, a new screen (that one a month ago), only to discover I CANNOT POSSIBLY CLEAN FROM MALWARE AND STAY CLEAN...
There is nothing I'd like more than to clean from trojans but seeing how the situation is I must stay in the internet, working around them, yes.
Hackers want very much to keep me out of the net and during the last event, the screen, I should not have replaced it and they had have succeeded but I won in lotto 15 euros and deposited them in my credit card, thus I bought a new screen by 20 instalments of 15 euros...
Sorry for my english, it isn't my native language.
Whenever I asked for some antitrojan program cd-rom in a box locally, sellers, users and experts considered me as lunatic and insisted one only risks trojans when visiting somehow illegal sites, they insisted there isn't such a thing as antitrojan.
I searched in pcmag and pcworld online and found spysweeper which was sold unbelievably locally too, yet this program is completely useless against trojans.
I have Nod32 and Zone Alarm Pro, except for Spysweeper and I believe they are all corrupted from trojans as they do not discover them, but only if I unexpectedly update some extra program as Spybot and scan, I find them.
At the moment I write you, hackers do not let me to connect through my last prepaid card and I must use some "free" connection that is a local call ten times more expensive than the card.
This is the permanent situation the last months so that my phone bill arrived huge and I was obliged to settle payment in 3 segments. I have my bill analysed and know that's all they do, no hidden calls elsewhere, just they stop me from connecting through the cheap connection and I'm obliged to use the expensive one...
"I want to keep them", don't make me lough, please...

I do not see a problem if you can get on internet now. An ASDL line will just let you surf faster.

The only problem if one would come up is if you open IE and cannot access the internet with the ASDL.

I remember some time ago, a Microsoft update conflicted with Zone Alarm Pro and made same thing, I was connected but had permanent access denial, that is I was connected all right but could not surf.
Before to find out what was it all about, a nightmare. Then another one, in order to manage to avoid the redownloading of the Microsoft update before to install the Zone Alarm update, I was restoring system to some days ago, then adjusting the windows updates time some hours later, in order to have the time to download and install the ZAP update...
10 years now I have of course forgotten all the details of security problems and consequent access problems...
But fast internet is not included in my experience that's why I ask.
So you say, maybe with fast internet I'll have total access denial because of trojans?
But I almost never surf with IE, same could happen with Firefox also?
Once I was tempted to pass to linux because of malware...
Then I thought I may very well ignore them.
I try to connect with my cheap connection and am denied, I try again, once, twice, in the 5th or 6th attempt I'm accepted, they are so ridiculous, believe me, and there isn't even one (number one -1-) time I didn't achieve what I was trying in the net because of them.
Only that I'm tired and surf a lot less now than before...

You should run into fewer problems with Firefox than IE

There was an update with zone alarm a few months back that did make it not able to connect to internet, zone alarms' fix was to update their zone alarm software

Zone alarm 7.1 and above have fixed the issue with the Microsoft update

You should not have a problem with a faster service at all other than you may experience now - nothing will change except how fast you can browse internet

Using Firefox will give you less if any problems