Did you remember to ???
If the old kernel works with X and the new kernel doesn't, it implies that you haven't installed the NVIDIA graphics drivers for the new kernel.
Each kernel caries it OWN set of drivers, so when the kernel is upgraded or recompiled, drivers that are not part of the standard kernel distribution must be installed again. This includes Nvidia graphics driver, nvnet, and some sound drivers.
If you are re-installing the Nvidia X drivers from the NVIDIA_kernel.1.0-XXXX.run file, be aware that it will REMOVE the X driver in the working (old) kernel. So, I would suggest that you make a copy of nvidia.o located in the old kernel module directory and copy it back to that location AFTER you do the Nvidia graphics driver install for the new kernel. That file can be found in /lib/modules/2.4.??-?/kernel/drivers/video where the ? are the numbers from the old kernel version.
Since the NVIDIA_kernel...run program assumes that you aren't running X, you'll need to boot into the new kernel in single user mode. In LILO boot, enter text mode and type the kernel name followed by the word "single". Install the driver and re-boot. example: linux-2.6.0-test4 single
Windows only keeps one copy of the kernel so it is not often that the graphics (and other drivers) have to be reinstalled but the *nix's have the ability to have multiple kernels available for booting ;-)
Hope this helps - (and that my diagnosis is right so the rest isn't an insulting discussion!)