I've had this exact same issue; I actually opened up one of my two gifted from bigger/older bro who owns his own graphics design and animation company - Avatar Labs - because it went through a flood and, to my surprise, had very absolutely no water damage at all, 'cept some rust colored stuff on the outside of the case here and there, but perfect overall, though the DVD drive sounded rusted out initially but after a month or two it all of the sudden started initializing at boot faster and eventually read DVD's, pretty interesting and sweet. It's a miracle! No, but cool.
Ok so, that's just a back story, sorry, fact is I've had the same issue after opening up one of my Minis and I'd bet $100+ that the DVD drive cable just isn't in **ALL THE WAY**. I opened it up after Googling your exact issue, refitted it, still didn't work.
Then tried it again, but this time since I accidently broke the very small plastic retaining clips that I thought came off a different way then they really did (I know I know, rule of thumb *never* force anything regarding computers), so I took a piece of strong tape and held the cable in place and now works perfectly.
I *HIGHLY* doubt anything's fried as I honestly have worked on PS2's, Xbox 360's, Xbox 1's, completely rebuilt and cleaned out a PowerMac G5 (took all out including the Mobo and procs from their sockets), Mac Minis, and numerous PC's and have *NEVER* fried anything and have *NEVER* used one of those wrist straps. Ever. Never any issues. I think as long as the parts are placed intelligently and handled w/ care, you should be fine.
So I'd just try checking the cable - multiple times if necessary - before assuming anything else. Let us know if it fixes it?