BMW: 86 325E starting problem, jumper cables, jumper wires

Question
Hello, I have an 86 325E that is giving me a hard time. The car has been parked for a year and last time it was started, it fired right up and ran fine. I replaced the battery and now when i turn the key to start the motor, the motor doesnt spin at all. It seems that if i hook jumper cables up to it that it will then start spinning but wont fire. Sometimes even with the jumper cables hooked up i turn the key and the motor doesnt spin. I can turn it off and on and play with the alarm and then it will start spinning again. I am getting ignition because if i spray starter fluid the car will start and die. At wont point the car fired up and began running, but it looks like something is cutting the fuel off because it will just suddenly die like it lost fuel. I dont think the coil is cutting out because it will start with starting fluid but wont stay running. It seems when the fuel pump kicks in the car runs ok, but it's like the electrical system or the computer just randomly cuts the pump off.....any help would be so much appreciated. THank you

Answer
Paul,
 Great job so far, you checked all the usual things, but in doing so you've answered your own question... you know the car is getting fire(spark), so it is DEFINATELY not the ignition system.  Second you've narrowed it down to fuel delivery (or lack there of).  
 So now I would pop out the back seat, pull the inspecion plate off (4 screws).  and try to run jumper wires to the fuel pump to make it run by it's self.  (WARNING!) Check for gas fumes first, stick your nose down there at the inspecion plate to smell for gas, if you smell it, you have a fuel leak, on top of your pump not working.  If everything checks out ok, pull wire connector off the fuel pump, and then touch 12v and a ground to the two prongs, if you hear the pump running it should be fine.  Second, check the external pump to make sure it's running.  These cars "should" have a dual-pump setup, with one IN the tank, and one in front of the driver's-side rear wheel.  make sure both are running properly.  
 If they both run, then it's a wiring issue, as something is not sending power to the pumps.  I would check the fuel pump relay next.  These are known to stick on occasion and cause the fuel pumps to cut off.

 Hope this helps,
 Josh