What you're describing is almost certainly an electrical problem (or two). It sounds like two things are happening and they are quite likely related:
Something is causing the engine to shutdown (your may find What can cause a gasoline engine to suddenly & mysteriously stop helpful for thinking about what could be happening).
Something is causing the starter motor not to run, or perhaps something is inhibiting the starter solenoid from pulling in.
Since these things happen together, I'd start by looking for a common element. Some things to check would be:
Grounds – especially if any of them were disconnected in the process of doing the rebore. Was the engine taken out of the car? If it was the grounds to the block should be double checked.
Common points in the circuits that support the engine (ignition, fuel delivery, ECU) and that control the starter.
If you can check, see if you see a start signal to the starter solenoid when you try to start after the car shuts down – this will help you determine the cause. Measure between the small terminal on the solenoid and the battery to eliminate the ground as the possible problem.
Aiso double check that the car appears to have been put back together correctly – for example if a heat shield was left off from around the turbo it could cause nearby electrical components to malfunction (perhaps there is a self-resetting circuit breaker that is overheating and "mistaking" a hot environment for excessive current).
In general, I think it is more likely that there would be one common cause for the two problems than that that two, related, problems have suddenly cropped up, but if the engine was pulled to do the rebore it is possible that there are multiple issues and they just happen to be related. But, as a starting point, I'd be looking at common points in the circuits.
