|The version of browser should have very little impact.|
It is likely that you need to reconfigure internet access under Start --> Programs --> Accessories --> Internet Tools --> Internet Connection Wizard
IE 5.5 should work without a problem. I routinely access the internet on my older machines, one has Windows 98SE and uses the built-in IE 5.0 browser. I'm actually surprised how well IE 5.0 still works after 11 years.
None of these old browsers seems to have issues doing casual browsing and logging into Computing.net.
The only downsides are as mentioned above you need at least IE 5.5 or Firefox 1.5 to access secure internet sites like online banking. And Internet Explorer versions earlier than 4.0 Beta 1 do not support PNG image files; while most sites still use JPG and BMP images, Wikipedia supports PNG pictures, so these won't display in earlier browsers.