I recently removed an old Sound City 120 power amp that had been sitting in my unheated shed for about 8 years (I think that was the last time I used it). What needs to be checked or done before I power it up and see what happens? Before it went into the shed, I had been using it a few times a year.

It will need to be cleaned, and checked for moisture, and damage from moisture. You really need to take it to a tech. It will probably cost you an hour's worth of labor. Probably around $50.00. It may cost more, if there are problems found.

Swain's right, but before you take it to the tech:

1) I'd just put it in a well heated room of a day or two (!! a 'moist' amp will cause only problems, and you'll end up paying extra money to the tech)
2) Then fire her up (hooked to a cab!), and let her warm up for a while on standby,
3) then switch standby to 'play' and see what happens.
4) plug in and play

stop if you smell/hear funny things.

I'd use a variac to power it up slowly. Those capacitors need to re-form slowly.