Hat can be used to get a DNA sample to hopefully identify the miscreant. Although depending in what you've done with it it's probably cross contaminated now. And I doubt (depending where you are) that this particular offending would reach the 'cost' threshold of getting it analysed.
As for the rest of the post - I'm with the others - see if you can work out some sort of deal then move on to a new laptop.
Most personal contents insurance policies cover your own personal mobile devices away from your home address. Just depends on the level of your excess whether it's worth claiming or not.
The current status is you decided to go ahead with the screen replacement as per the original quote. Is that correct?
If you want more information than you have been getting I suggest talking to the service manager a.s.a.p. It is unlikely they would proceed with the repair if they know it is not going to make any difference.
In any case parts can be returned to suppliers for credit most times etc so it may not be impossible to backtrack. It is easy for posters here to assume mainboard replacement is because the mainboard is 'fried' but the reasons for the recommendation/desire/need to replace it in this case may be different.
To add to the speculation, it may be the case repair cannot be guaranteed without doing that, hence the desire to do it.