Good one. You need not have done a reinstall just to clear spyware but that's another thread.
Your PC spec won't stop you connecting to the Internet unless your modem states otherwise.
If it worked before, it should work now, so my guess is either/or/both: the Internet connection is not set up correctly - the modem software is not installed correctly.
It is not likely spyware would remain after formatting/reinstall.
I know nothing about UK BB connections but surely it's not a dial-up modem as they are usually for 56k connections? Usually one just plugs the BB modem into the phone line and that's it - it doesn't dial out as such. If you do have a dial-up modem fitted to your machine, and is necessary! - have you re-installed the driver for it.