A few weeks ago I tried to make an account using my old school mail, but it turns out it has a problem of some kind, and so does not work. So instead I now tried to make a new one, with my father's work mail, but I did not get the mail that is suposed to activate the account. I was wondering if this had somthing to do with this being my seckond request from the same computer, and if so it would be possible to delete the first account (which I can not access)?
No, something like that would not prevent you from receiving the acceptance or rejection e-mail. It is more likely either that you misspelled the e-mail address the second time, or that it is blocking or deleting the e-mails as spam, as a number of e-mail providers are known to do that. You can follow the instructions in the "Problem: I haven't received my password!" thread to have it re-sent and to narrow down the cause of the problem.
Only one existing account displays for your IP address, so if you feel you may have a second account you need to provide the handles or e-mail addresses with which you have attempted to register, both previously and recently.