I'll chime in here as well. I don't agree with the CPS being bad in this particular scenario. A failed CPS will not prevent the car from cranking over. You can take the CPS completely out of the car and it will still crank over, it just will not fire up.
I agree with Paperplane with a couple of additions. Your neutral safety switch in the transmission (assuming you have an automatic) could be a little buggy. Next time it happens, switch the transmission to neutral and try to crank it. A failed neutral safety switch will make it just like you are trying to crank the car in drive, i.e., no response from the engine when turning the key. All lights will light up normally as well.
Another, and less pleasant possibility, is that the EWS II is beginning to fail. This is a security system specific to the 1995 model. If it activates, then you will have the exact same scenario as you have now. There are a couple of ways around it, but the easiest is probably getting a chip to put in the DME that bypasses the EWS II system.
Check with Supertech777 on this fourum. He did it on his.
I had to bypass the EWS on my E36, but it was because of a bad DME, and the wiring colors were a little different. Supertech777 has done it on his E34 and should be familiar with the exact wire colors.
Hope this helps.
Most problems are usually something simple !
Originally Posted by noego
It's Deja Poo - as in, I've heard this **** before.
Calypso Red 1992 525i with 225K miles
1991 735i - Sold
1992 525i - Sold
1995 325is - Sold
2000 528i - Sold