Can you force Apple to fix iPhone?

Here is the thing, I installed iOS 7 on my iPhone 4 and now it's not working anymore. It lost it's serial number durring instalation and I took it to the shop and they are fixing it for like two weeks. They told me that they probably won't be able to fix it for some reason I did not understand.
What my question is can I make Apple fix this phone, even if it's not under waranty.
They said iPhone 4 is compatible with iOS 7 so isn't this their fault?

Just cause something isn't under warranty doesn't mean the company doesn't want anything to do with it. That seems to be a misconception as of late. All it means is you'd have to pay for it to be fixed, but it still will be fixed if that's what needs to be done.

If it can't repaired, it would likely be replaced.