I'm guessing that if make bzImage gave an error that it was too big, you're newly compiled kernel simply isn't going to work.
I'd do a couple of things
1) Make copies of your old vmlinux and System.map so if your next kernel also goes kablooie, you still have a backup. After learning the hard way, I now have a vmlinuz.good and System.good that I can always use.
2) Did you actually name your kernel bzImage?
in my lilo.conf the line is
as far as I know, just using the standard compile creates a kernel called vmlinuz, not bzImage.
3) Head over to the Slackware section of the Distribution forum. DaOne has posted a very good explanation of how to compile a kernel including how and why to use make install
after make bzImage.