Right, well, a few days ago, I got a new router. It's been quite troublesome ever since (signing me out of Windows Live Messenger due to it disconnecting).

Earlier on, a contact sent me a large file. It transferred fine. Now, about half an hour ago, another contact sent me a media file- not too big, around 4000 kb. It began to transfer, VERY slowly, 1 byte at a time, until, eventually, it stopped, and I received a message that there was an 'error in transfer'. Was this anything to do with my router?

Well you can try getting it transfered on you normal modem if you have it and if it works it will be the router.

That sort of thing used to happen to me, too, but it's nothing to do with the router. Usually it's when the file itself has an error in it. for some reason it affects transfer...

Anyway you can stop worrying about your router, it's fine.

Make sure you have UPnP enabled on the router. If you want you can DMZ your computers IP address (making sure you have a firewall active as DMZing your computer means all inbound traffic will be forwarded to your computer.)