Mark:
Whether or not the wrong chemical was applied would depend on how fast the turf died and if there was any type of pattern created immediately after application. Usually a chemical burn shows up right away except for a systemic product such as Roundup. As far as finding any in the soil - you'd have to get the soil tested for specific chemicals something not "usually" done but a soil lab would be who to ask about it if you can find one.
As far as other culprits for it's demise....I'm a warm-season grass guy so am not too familiar with your grass variety's culture. You could Google your grass variety (example "Fescue" or Bluegrass") and see what issues it has and then try to match up what actually happened to what it says in your Google search.
The advice about contacting your county agent is spot on - that would be a good start.
If you have a Lesco
Welcome to LESCO.com store nearby - they sell turf care products and may also be able to help. They were bought out by John Deere but still go by Lesco on a lot of their marketing stuff.
On the question of drought - it would depend on if you have and use an irrigation system PLUS the variety of turf you have and what it's irrigation requirements are PLUS your historical rainfall conditions.
I wish I could tell you what to do to restore your turf - a Lesco rep would know if you could get a hold of one. They would also be able to steer you to a reputable turf care specialist or provide directly to you what's needed to do it yourself, if that is of interest.
Good luck and keep us posted!