iTunes authorization problem

I had a hard drive malfunction with my old iMac and just bought a new one. The old computer won't turn on, so I cannot get into it to deauthorize iTunes. And I cannot authorize the new computer because of that.

What should I do?

Should I deauthorize all computers and then authorize them one at a time again?

If you no longer have access to the machine that you wish to remove authorization from, that's what I would do.