Enabling agp ("NvAGP" "1") won't help since he has problems now. Before you try anything else upgrade your driver version.
"I'm running Debian 3.0 woody, linux 2.4.16 and Nvidia module, 1.0.2313. I know they're not the latest versions. But things are working fine for now."
Apparently the drivers aren't working fine. After driver 1.0-231x nvidia released three new driver versions. The latest one is 1.0-2960. Soon there will be a newer version again.
It is really important to try another nvidia driver if you have problems. Nvidia's drivers aren't allways that stable ....