ukm 13,
Here's an "official" minimum system requirement for DVDFab in Blu-ray mode:
* Windows 7/Vista/XP/2000 (32-bit/64-bit)
* Pentium II 500 MHz
* 512 MB of RAM
* A Blu-ray Drive
* Internet Connection
However, it's really boiling down to your understanding and definition of "backing up". If you mean and intent to just rip the entire BD onto your HDD (or external HDD), specs of your older PC is good enough (you do need a BD drive though). If you want to convert and compress your videos, it will work too, but very very very slow. If you have luxury to set DVDFab for process and leave it for a couple of days, it will work for you. Considering age of your "older PC", problem with some of your Blu-rays ("it will either close or it wont read it"), most likely lies in your hardware. I mean, firmware of your hardware could be very well outdated and requires an update. Please try to update firmware/drives for all your devices.
Oh, BTW - this: "I'm willing to upgrade my older pc to meet the requirements" is not going to work. If you want to have a decent machine - build new one.