The trip odometer has 2 bulbs and it sounds like one or both are working intermittently on your Q. The speedo cluster is going to need to be removed to replace these. They're available for about $11/ea from the stealership or you can by just the 12v bulbs from Radio Shack, 2 for $2, and insert them into the holder yourself. Easy stuff.
The HVAC controller display going dark is a common problem in the 90-93 Q and is a little tougher fix. Search out a thread by Q451990 (Heath) for the repair instructions or email/pm him and buy one of his repaired units for a very fair price.
Your Q has been sitting for 4 years so I'd suggest pouring a bottle of Redline S1 Fuel System Cleaner ($8) into a 1/2 tank of gas to make sure that the injectors don't get plugged with residual varnish from old gas. You can find Redline at Pep Boys or Napa Auto Supply for sure and probably others.
Welcome to NICO!!!