Do you have an antivirus on it with latest definitions? Just odd that you cant get out through ethernet and programs are closing on you. I've seen DoS ( Denial of Service )Virus's eat up all bandwidth and cause no internet and programs to either not open or kick out.
Either way, I'd say you are looking at a rebuild. And if a virus is present, you will need to clean the data if important and infected.
Easiest rebuild is if you have a system restore CD set and an extra hard drive or were planning on a HD upgrade, this is the perfect time for that upgrade. Install clean new or used HD and remove old HD, Install clean OS, and then install latest AV with latest definitions and either introduce your original HD back to the system as a slave drive or get a cheap bare external HD case and make it into an external drive. Then scan the drive. The USB method is the safest, since if you waited until your system was booted off the new HD and Real-Time AV software was running you plug in the external HD and if anything tries to make a move at the clean drive it should be shot down by the AV. Plugging the drive in as a slave, could pose a creep of the virus before the AV service has started. I would also suggest makeing sure that all works perfect with internet etc before introducing that drive, just in case after you introduce it you see the same results. If the same results are found after you know that it was behaving and now once again its cant connect to the internet, maybe a new virus creeped into the new HD.
Other tell tale sign of a DoS virus infection is that your network connection will show lots of activity broadcasting when nothing should be going on. Also if you look in the Task Manager you will usually see the CPU pegging to 100% at idle or a heart beat EKG appearance on the graph with equal interval spikes as the virus is in a broadcast loop to try to spread to other computers on the network and out on the internet.
Good Luck!
Dave