Shock.. Wont start

Hello:

what an interesting forum..

I have a 1985 500SEL (63 Original Miles)

I had the car for about one month.
today I went and washed the car in (30 Degree temp) and parked it in the garage... after 1 hour I tried to start it and I got shocked.. Car wont start.. it cranks but wont start
The car has new battery (from the shape of it)
I was reading some threads and people were saying it could be the fuel pump or fuel pump relay

please if you can direct me to exactly how to test either. I am not a mechanic, but I have a mechanic friend who will help me diagnose..

I appreciate your time and help

Thanks