Schematics help you troubleshoot further but if you do not have the ability to power up the board, you are limited in how far you can go with your troubleshooting.
One solution to this problem we have used is this: The customer agrees to pay for 99 boards. The final board is scrapped with the assembly house "eating" the cost of the scrapped board. If the customer truly needed 100 boards they may not agree to this but in that case they should have ordered a few extra to begin with. The catch is that if it is a high $$$ board getting scrapped it may eat up a large portion of your profits for that job. If it is a small board not costing much this approach may help earn repeat business from the customer.
From your description it appears the problem may be a bad component or the bare pcb was bad to begin with. It would be nice if they would do some troubleshooting since they know the board better and can power it up. Then they can come back to you and tell you which part needs to be replaced. That way you are only "eating" the cost of that one part, and not scrapping out the entire board. Sounds like they are not willing to or can't do this.
We have had customers who were fine with scrapping the one board and customers who did more troubleshooting on their end. We have also had a customer who refused to do either (they insisted we get them 100 boards that worked without any troubleshooting from them but we had no way to power them up to test) and they are no longer a customer of ours. Long way of saying that I don't think there is a basic rule; each situation gets worked out differently.
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