You might want to image the disk on the old computer. If for any reason you crash, Money will ask for the password, even on that old computer. You will not get in without a password.
Also, write down any passwords that you might have used. Write down anything you can remember about the password.You may remember the password in the process. Also, check places where you might have written down your password.
One more thing: I would export each of your accounts as a Loose QIF file. That way you could import them (all at once) into a new file. This could be used to migrate you to the new computer, or you could just save those files periodically in case your old computer
crashes-- or if Money wants you to enter the password again. So while you have access, I would consider that. If you want some QIF export+import tips, say so.