If there is an operating system currently installed (and working) on the computer, you can use it to tell whether your processor is 64-bit or not. The method depends on which OS it is. On Linux, go to a command prompt and run the command
uname -m, and if it prints
x86_64, you have a 64-bit processor. Anything else means you don't. On Windows, I don't remember offhand but probably if you right-click My Computer and choose Properties you may find it in there somewhere.
If you don't have a functioning OS, you can probably get that information from the BIOS. Again, it depends on which BIOS you have, but usually there will be a notice that appears immediately when the computer starts up that says "Press F2 for Setup" or something like that (sometimes it's a different key, like Delete). If you hit that and poke around a bit in the menu that appears, you may see something that identifies your processor as 64-bit or 32-bit.
Also, I would agree with what nhinkle said about checking the integrity of the ISO image and of the burned CD.