I believe EWS/key issues would prevent the fuel pump from priming. The first diagnostic step is to fully charge or jump the battery again. You may have a parasitic draw, or an alternator that isn't charging to the proper voltage. 11.9V is a little low.
The next diagnostic step after that is to rule out the ign switch by checking the current of the small wire going to the starter when attempting to crank. My guess is that the starter itself is bad. Or, try to isolate that buzzing while having someone turn the key. If it's coming from the starter (more accurately, the solenoid), I'd be pretty confident in installing a new, not remanufactured, starter.