Does your new kernel start booting and hangs up during startup,
or doesn't it start at all?

If you misconfigured your kernel, it might happen that some things don't work - like network, soundcard, ... - or when you forget to include the code for using the ext2-filesystem, the kernel won't be able to mount the root partition (for example : /dev/hda1). Your linux system won't be able to start up. This are just examples of what can go wrong. There are a lot more reasons it might not work. I would advise you to check the configuration files for your kernel.

Another possibility is that the kernel didn't finish compiling. Due to misconfiguring or because the kernel is too big (this can happen :-) ). If your kernel is compiled (command 'make', without options), it should end without errors.

Maybe something went wrong when applying LILO. If you execute 'lilo', a list appears with all possible bootoptions. The default bootoption gets a star (*). If this list doesn't appear, or when an error message is present, your MBR wasn't changed, so it will still boot with the old configuration.

Please excuse me if I misinterpreted your descriptions. I hope this will get you on the way...

BTW: I use kernel 2.4.19, without any problems, so I suppose 2.4.20 should work allright. Unless you have just discovered a bug ... :-)