Cannot login

Hello,

Recently on another computer we went to a website which apparently dropped some viruses on our PC (using XP). After running the virus scan, we removed the viruses. Following that, the computer was restarted, only now the problem is we get to a login screen it is now asking us for a password to log in to the account

The problem is we don't have a password on this computer, and havn't for months. We tried all possible passwords we've ever used on this computer and previous ones, but to no avail.

Upon starting in safe mode and attempting to login via the administrator account, we were again prompted for a password, even though there is no password for the admin account

Apparently right before the computer was restarted and these problems began, going online to google caused random popups to spring up from nowhere; whether this is related or not i'm not certain

So my question is, is there any way to get into the computer without the passwords, or any way to get in that WON'T result in all applications needing to be reinstalled?