Keep crashing on Internet

Bought a used Dell computer w/Windows 2000 Professional (never had a home com puter before) - have Verizon DSL broadband service - I have what seems to be called "intermittent connection" problems. I'll be on internet okay, then suddenly screen goes black and automatically reboots; desktop eventually comes back on just like as if I just turned it on; then I can click on Internet Explorer again. I have changed the filters Verizon sent for installation; I have defragmented; I have pulled plug out of modem and put back in; I have pulled out the jacks on my other phones even though I put a filter Verizon supplied at each wall jack site. Is this because I have Windows 2000? Or a 4 year old Dell? Is the only solution to just buy a new computer (I see them advertised for $400 or $500 - I only need something basic, nothing fancy, just to be on the Internet at ngiht after work). Thanks for any advice.