As I just told you, Q has nothing to do with mIRC. You paid for mIRC, which is the client you are using to connect through networks such as QuakeNet.
You are not paying the networks you're connecting to. None of the money you spent on mIRC goes to QuakeNet or Q for that matter. Q is a free service.
If you have problems with Q, you should join the #Help channel and ask for help there. The people that manage Q, and thereby can solve your problem with logging into Q are there, not here. They can fix your problem.
As for your mIRC 'details' (Which, may I rephrase again, have NOTHING to do with Q), if you forgot your mIRC key, you can always retrieve it without having to purchase another copy.