My phone screen had went out. How do I transfer my old game to my new phone. I do not have my account number
The only ways that I know requires things being done ahead of time: backup up iPhone on another computer and do so frequently, or have an iCloud that does the same thing.
Doing it after the fact requires having someone fix your screen first and then copy the information over because when you transfer the information the iPhone will ask that you enter in your code first to approve the connection for data transfer otherwise it will refuse. You will either need to get someone who is really tech savvy to do it or you are going to have to get to an Apple dealer rep to have a technician do that for you (which might be costly and some people are rather cagey about letting other people have access to their data).