Volvo S40 2007 Crank/No start

So, I drove to school today, and the car was running fine, and when I came back to my car after school it would not start (engine starter didn’t start). I switched the R13 (which is the engine starter relay I belive), and it starts to crank, but the engine would not start. I switched between two of the relays, and then I find out that the engine relay (R13) had a broken connector pin. Now the engine starter runs, but does not start the engine itself. Last week the same problem happened, but I just hit the fuses and relays in the fusebox, and the engine started again. Something tells me that the broken connector pin is the problem, so I went to Oreillys and bought one which is simular to the one in my Volvo S40 2007, but its not the same (same voltage and dimensions though). Same problem happened; cranks but does not start.
Do you guys have any idea what can be wrong with the car?

Thanks!

The best path is to focus on whether it is happening b/c of no spark or no fuel.
ask you shop to verify you get a good healthy spark at a spark plug during cranking.