If you don't have your old passport you need to try and remember any time you gave it to anybody and see if they have it.

did you ever keep a copy in case you lost it?
Ever use it to get a job and they kept a copy?
have it in an airline's profile?

If you can't figure out where you may have the number, you can try the state department, though I'm betting there's no chance of them having it for you by next week.