When surfing the internet, I keep getting asked to "connect". Sometimes I can push the "connect" button and things continue on just fine... other times my dial-ip connection window keeps popping up, and I am unable to move past this point. I am currently using adsl. Why would this happen?

You have picked up a rogue dialer and need to scan you system for malware and viruses as soon as.

System maintenance includes:
Defrag
FULL patching
Virus scanning
Spyware scanning
Removal of rubish files

Defrag is an inbuilt function in XP.
Open My Computer > Right click C: > Tools Tab and it's there.

To make sure everything is running fine run both anti virus and anti spyware apps in normal AND safe modes. (make sure that they are updated first ! ;)) (AVG is good and free AV)
(A couple of good removal tools are Spybot and Adaware)

ALso an on line virus and spyware scanner is Trend Housecall

Just a note; actively running two AV's on one machine can cause problems.
So if you are thinking about it make sure your current one is disabled first.
Same thing applies to online scanners as well.

Removal of junk files is easy with CCleaner a free app that does exactly what you neeed.

It might be simpler. Go to Tools>Internet Options. In the Connections tab make sure its set to Never Dial.

Good idea there Scott, but rogue dialers don't take any notice of this setting ;)