92 E36 DME and ground magic

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My 92 325is couldn't be started and the mechanic told me that camshaft and crankshaft position sensors were bad. Then the fuel pump was bad and had to be replaced too.

This apparently still didn't fix the problem because he told me that the computer didn't have ground on the DME relay so he ran a wire from ground (body) to the relay which basically makes the car think that ignition is on.

He says that it's the computer that's busted and I need to replace it.

Does that make sense? I don't know what to do at this point. The car runs but I have to disconnect that ground or the battery dies. This is wonky!

I took the DME out and will look for replacement but I just wanted to hear your opinion on this.

There are many numbers on the DME. Is this number the identifier and the rest don't matter: 0 261 200 413 ?

Thank you for your help

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I got a refurbished DME off eBay and replaced it today but that didn't fix the problem.

This is weird stuff. Maybe the relay itself is bad but the mechanic said he tried replacing it with another one and it didn't fix the problem.

When that ground cable is unplugged the car just cranks and doesn't start but as soon as I connect it, it starts without a problem.

Any suggestions are welcome!