I just tried two of the MagnetMix files while disconnected from the network, and they both started downloading almost immediately.

So there is definately some really blocking Limewire.

MagnetMix is a site, so when you download a magnetlink from them, the info needed to start the download is allready in the file.

Maybe your router is getting old and wants to be replaced by something like a Billion BiPac 5200

I had some routertrouble myself before I retired my old one (SMC7204BRA) stay away from that one and also the SMC7904BRA which I tried as well

Try borrowing a router from someone, to see if yours is in fact is a goner