I assume grub successfully compiled, you can get to a grub prompt from within slackware and that when you run grub-install from a console the command never completes, i.e. it hangs. Further assuming you have successfully edited your menu.lst file to boot your slackware installation, try opening a console and running as root:
which sould take you to a grub prompt if grub is properly installed on your system. Your console should look like so:
At the grub prompt run:
grub> root (hd0,0)
grub> setup (hd0)
assuming slackware's kernel is installed on /dev/hda1 which is (hd0,0) in grub speak. /dev/hda2 would be (hd0,1), /dev/hda5 would be (hd0,4), etc. I further assume that your bootloader is to be installed on the mbr of hda which is (hd0) in grub speak.
When these command have successfuly run, type:
to exit from the grub prompt.