NO ONE can tell you what is going on with the car, but I can say that there are several possibles here:

1) Unstable/low system voltage due to a failing battery and/or alternator. This explains the wing acting funny and no starts but only possibly explains not getting out of park.
2) Traction control relay output is failing, this is an RCM failure. This explains the wing and not getting out of park but not so much the no start.
3) Lousy ground connection between the battery and chassis OR between the block and chassis OR really cruddy connections at the battery.

Why can't anyone tell you what is going on? Because...........
Telling us "it would not start" is a sure way to waste your time and ours. That is an ambiguous statement. What we want to know is this:
Did the car's starter engage but the engine refused to start, or started and died?
or...........
Did the starter not even engage?

Above are two VERY different failures and which one you had, combined with your other information, tells us a lot.