Run the ECU codes
http://www.allpar.com/fix/80s-codes.html I doubt its vapor lock.
When it doesn't start do you hear the fuel pump running, is it getting spark, and is the engine cranking?
By the entire underside being covered with sheetmetal, do you mean that the underside of the car is all flat sheet metal with absolutely no fuel or brake lines or the exhaust system exposed? That is not normal for any stock Dodge, it might only be stock on extreme high end performance cars. If you could gets pics could you post them.