The problem is not with GRUB!!!!!
If you can see the gui terminal presented by GRUB and select fedora then GRUB is not the problem here. Installing LILO will not help!!!!
Lots of possibilities:
1. The kernel 2115 doesn't work with your hw.
2. There are certain services that is causing a conflict.
Edit the grub configuration for Fedora (press e after selecting fedora)
Select the second line that contains the kernel keyword then type e again to edit.
Append "S" to the end of the line.
Press Esc then b to boot into single user maintenance mode.
If you are able to reach the # prompt. Then most likely you have some services that doesn't work well with your machine. Check the log files in /var/log for error messages.
Hope this helps