The shop sounds like a bunch of idiots..There is like 1% chance its your ECU. I have an extra ECU to my 92 5sd GS. Worse comes to worse I will mail it down to you and you can see if that is your problem (provided you do it yourself so your shop doesnt charge you lots!)
First off - check the starter, and all wires to it. If the lights are working its not the battery, but starter turns the car on!
Check grounds, specifically the starter ground and alternator ground.
Did the engine TRY to crank over at some point then stopped?
Im 99% sure its a wiring issue seriously, check all the wires to your starter and disty...why would you change the disty if the car wasn't even turning over!

The shop seriously recommended this? You should get your money back! Thats total BS - I would be pissed!
Please give any more info