Chosen Solution

On start up I get 1 second white light front of the mac mini then immediate shut off. When i press the power button again it does the same. RAM or HDD still works tested.

This doesn’t sound good ;-{ I’m hoping your power supply went on you here’s the IFIXIT guide to replace it Mac mini Mid 2011 Power Supply Replacement and here’s the needed part Mac mini A1347 (Mid 2011) Power Supply - Apple P/N 614-0503 IFIXIT is out of stock so you’ll need to do a bit of searching. Where are you located? So we can aim you to a more local source. If that fails to fix things then your logic board is toast then its a matter of how much to invest. Keep in mind a new Mac Mini is expected before the end of the year. If you can I would wait to see what Apple offers up. In the mean time you can take your drive(s) out to recover the data to a second Mac system using a SATA to USB adapter like this one Startech 2.5" SATA to USB3 adapter