For us newbies (and that includes me too), here's what I would do. I would install the kernel but would keep the previous on that works for me. After installing the new kernel, I would check /boot/ and make sure the symlinks (is that what it's called?) for initrd.img, vmlinuz and config point to the same kernel versions. Meaning if vmlinuz points to the 18.104.22.168, check that initrd.img and config does too.
Then check /boot/grub/menu.lst to make sure that all those vmlinuz, initrd.img and config are on the same block starting with title and ending at img. Also double check that your previous kernel is intact in case the new kernel doesn't work on your machine, you can reboot back to the on that works.
The new kernel might take a while to install the modules needed to run your pieces (of hardware and driver) so be patient. Better if you can press Esc to go verbose mode so you can see what is happening underneath all those blues and greens. But if after TWO hours, nothing (and I mean nothing) improves, try it one more time with a hard boot. Note where the bootup had stalled and if on the second (or third attempt), hopeless is the only word you can think of in your mind, go reboot back into your previous kernel and post your report.
I hope I made sense in this post. I think I might have to look for Neal so I'd have someone to drink coffee with.
Good morning from China.