This could be hardware related but as you use the live cd I presume you've got it working in whatever you have installed. Still check carefully that your mouse and keyboard are properly connected.
The more likely candidate is your live cd. Check the md5 sum of the ISO and burn again at the slowest speed possible. There are always errors when you burn, taken care of by ECC code on the disk, but the fewer the better and live cd disks are sensitive
Don't fix it if it ain't broken, don't break it if you can't fix it