Mac mini not starting up

Sounds like the best guess at this time.

If that works, replacing a hard drive (either with another hard drive or a SATA-based SSD) isn’t too hard to do. There are a lot of steps, but none require any special training as long as you are careful to follow the instructions.

To replace the lower drive (or the only drive for a single-drive mini):

To replace the upper drive (or install a dual-drive kit to add a second drive) has a few more steps: