Perhaps you could more closely identify the Mac Mini because there
have been several builds under that name, & with different hardware.
• How to identify Mac mini models - Apple Support
Some model version owners had reported issues, so to know which
one your grandad has may be helpful. However depending on the
exact build model (year, graphics, CPU, etc) it may be easier to be
on the lookout for a different model. Or have an AASP look into it
to see if the hardware can be repaired at reasonable cost.
Integrated hardware fixed to the logic board makes some of these
newer most compact Macs most difficult to repair; yet there are
modules that could be swapped out in some instances. A good idea
is to look into the iFixit Repair Guides for Mac; and see the guide to
repair specific series your grandad owns. Gives you an insider view.
• Mac Mini iFixit Guides: https://www.ifixit.com/Device/Mac_Mini
Not sure what else to say; except depending on the Mac Mini build
year, there had been more graphic issues; and the GPU is affixed.
A thread of certain Mini issues (GPU) exists in ASC discussions.
Good luck & happy computing! 🙂