Can't reinstall os and erase mac hd

I have backed up all files into an external hard drive, inserted the install disk and tried to reinstall the os. Once the installation pops up I go into disk utility to erase the hard drive first, but it doesn't show up. It just says fujitsu or something, and the Mac hd partition is not showing at all. If I were to go to disk utility when the computer is working normally I see the same fujitsu drive, but the Mac hd partition is also there.

I tried to make another partition to install the os into, but receive be an error message.

I tried to just install the disk without erase the hd, but there is no drive showing up Tay I can install it on.

If I boot the computer without the disk, it works fine.. So I don't think the hard drive is corrupt. The machine just runs really slow and if like to start from factory settings.