This is MBR Lilo you are booting off?

For now it is MBR lilo I am booting from.

With the 3.7.1 kernel suspend works but hibernate does not. The problem with 3.7.1 is different than with 3.4.24. In this case it never shuts down. In 3.2.24 it shuts down but does the funny screen problem when trying to resume.

With EFI, if it supports creating new entry for EFI kernel, then you could compile your kernel with EFI stub built in, copy the kernel to the EFI boot partition, re-boot into EFI setup and add the new entry, then it could directly boot the kernel without an extra boot loader.

I could only get it working on my Dell Otiplex 390 with 64-bit kernel, it seems the EFI could not boot in to my 32-bit kernel directly.