Aye, I figured that was my problem. What I'm in the dark about is how to actually fix it (or where else to start looking) as I have barely any SQL experience at all. I was just told "Get a website working." and that was it.
Windows Firewall is actually disabled as we're on a domain with a dedicated firewall, and I wouldn't have a clue where to start with checking the MySQL config.
Launching the MySQL Command Line Client gives the error
Could not open required default file: C:\Program Files (x86)\MySQL Server 5.1\my.ini
Fatal error in defaults handling. Program aborted.
Enter password:
Entering any string (whether it be the password or not) causes the CLI to close without any further messages.