You do know that tarantulas moult on their backs right?! Dead Ts *often* just kinda slump over onto their sides with their legs curled underneath them but moulting Ts do it upside down...
Not denying that it's dead just be careful before you throw it away
If it escaped the shed, then it probably wasn't humidity or temperature... Did you have a waterbowl there?- Ts like to drink a lot before and after moulting. My guess is maybe exhaustion but couldn't tell without a full autopsy *kiddin*
She may not have been dead, Even after molting some Tarantulas will spend a few hours on their back 'Recharging', Molting is a very strenuous time for a Tarantula you know!
lullaby10 do your T's go nuts when you mist them? :shock: You may be stressing them and not know it. You don't really need to mist them if you offer plenty of fresh water in a bowl. Even "high humidity" T's can live happily in a bone dry habitat with a water bowl always full. Just my 2 cents.