Potential trojan; can't log in in safe mode

[Trowby]

Was on the internet and somehow received a virus. It showed red flashing
text near the icons in my display window saying something about
trojan...it was asking to install and run some kind of anti-virus program.
I didn't know what it was, so I turned the computer off. I restarted it in
safe mode and I get to the log in screen (we're on a network and each user
has to log into their computer), but I can't log in under any user name.
Also, now when I reboot, I can't boot in normal mode. It always boots in
safe mode and I can't get past the log in screen.

I've been advised to write zeroes to the hard drive and reinstall Windows. Is that the right move? Does anyone know what this is that's infected my computer?

[moviscop]

It often doesn't matter. If your computer is that messed up a reformat is always a safe bet.

Usually when you get a virus it phone's home for more viruses to be sent to your pc; it is a mess.

Unless you have data you can't lose reformat if you want to save yourself a headache.