Why can't I access any websites?

I have two machines, an older machine running Windows 98 and a newer machine running Windows XP. For the last few days I have been having difficulty accessing the Web, primarily on the 98 machine, but occassionally I have difficulty on the XP machine as well. Clearing the web browser on the XP machine usually solves the problem but it does not solve the problem on the 98 machine. The two machines are connected to the cable modem via a wired Linksys router.

I know that this may not be the ideal newsgroup to post this question as it primarily involves a 98 machine but this is where I usually post and people have been very helpful to me here. If you think I should post elsewhere, please let me know.

The problem: My 98 machine has great difficulty opening a web page. The only way I can get online with it is to turn off both machines, then turn off the router, then turn off the cable modem. Then I turn on the modem, turn on the router, then boot both machines. I can then get online with the 98 machine, but often only for a few minutes until I have to repeat the process again. As I mentioned, I can generally get online with the XP machine, but often to do this I have to clear the browser (delete cookies, delete files, clear history) and try again. The lights on the cable modem and the router appear as they always do.

I don't even really know if this is a problem with my 98 machine or with my cable service, or even if it is a problem with my cable modem or my router.

I ran Norton Antivirus, Spybot and AdAware on my 98 machine in Normal Mode. I ran Spybot & AdAware on my 98 machine in Safe Mode but Norton Antivirus seems to freeze in Safe Mode. No problems were found although SpyBot often finds an "Error during check" (even before this problem arose). If I reboot and rerun it, it runs without errors.

Any suggestions?