Manually Installing A New Kernel

"Exact details depend on what your distribution is, so you need to add that detail to your question, but you should be able to:

mount your filesystems from an appropriate live/rescue CD
chroot so that your are using those filesystems in that terminal rather than the live CD's
ask your usual package management tools (yum/apt/what-ever) to reinstall the kernel package(s)

Assuming, of course, that the missing kernel is the only problem."