Sounds like the NVIDIA_kernel installed, but the module that it uses isn't being loaded at boot.
Mandrake uses devfs, so make sure your /etc/modules.conf file has a line in it reading alias /dev/nvidia* NVdriver
When you see the flickering back and forth, hit Ctrl-Alt-F1 and log in (as root) in text mode. Then do a cat /etc/modules.conf to check what's in that file. If the correct alias line doesn't appear anywhere (others may be there, that's not a big deal), then do a vim /etc/modules.conf, arrow-key down to somewhere where you can add another line, hit the 'i' key (to enter insert mode), type out the alias line above, hit enter a couple times (for spacing purposes, no other real reason to do that), and then hit Esc (to exit from insert mode). Type in colon, then w, then q, and hit enter to save and exit. Then do, still as root, /sbin/depmod -a
Then, reboot (Ctrl-Alt-Del should shut down properly, otherwise init 6 works) and see if it works. It should.