I assume you booted into the install process with a Live OS (Fedora does that as standard).
My first approach would be to boot into a more forensic type of OS, such as GParted and do all kinds of checks. For instance check RAM, check hard drives, etc.
If your PC can boot from USB stick, I'd suggest using that, to rule out the CD/DVD-ROM drive is faulty.
For testing RAM, use Memtest86 and/or Memtest86+ (one is based on the other), if your LiveOS doesn't come with it in the bootloader anyway.
Just in case the problem is not exactly reproducible: If that's not a laptop, it might be a problem with the power supply.
If the PC freezes just like that, it might be a problem with the graphics card drivers as well. This usually doesn't apply to older hardware, but just in case, try booting into text mode and see if error messages come up. Fedora doesn't have the closed-source NVidia drivers. You have to add another repo to make them available. You could try installing Fedora in text mode, then installing the drivers, and then work your way from there.
You might want to try simply a different distro, as Fedora is considered "Bleeding Edge" and might come with some problems pre-installed... I advice booting into something like Ubuntu or Mint, or some other distro and just check if the installation process is working there (the distros I mentioned use a LiveOS to start the installation process from). If it does install fine, then it might be Fedoras problem of not playing nice with your set of hardware.