I've had this old Alesis Microverb sitting on a shelf since I bought it for around $20 in the 90's. It worked for about five years then just crapped out.. The power LED indicator lights up but no sound at all, nothing not even a clean signal. if I adjust the controls a bit there will be a flash of white noise for a second.

I've checked the connections and could use a recommendation on how to proceed troubleshooting this.

ya, I guess it's down to that. No big loss but I sort of liked using the reverse here and there.
I bought a Microverb II a couple years back for about 30 bucks. The pots were dirty, so I cleaned them. Still works perfectly.
I'd suggest giving cleaning a try.
..I was watching my death.