if you're fairly good with computers(but if you're not, do NOT attempt this) you can do the following:
START => RUN => regedit
once registry editor opens do the following:
expand "HKEY_CURRENT_USER"
find "Software" and expand it
find "mIRC" and expand it
find "License" and on the right side, it will say the following
(default) "####-#######"
that number is your registry number
hope that helps

(Please Note: this instruction is for a Windows 98 SE machine, and may not work on Windows XP)