Maybe I'm not understanding you correctly, but it sounds like Bitcoin Core is immediately shutting down for you?
Now, I'm no computer expert, but I don't think ISPs blocking traffic can cause programs to crash.
You are using Windows XP? Perhaps you should try another OS?
Have you tested your computer's hardware for stability?
I'd say I have a reasonably stable system, considering what I've added to the mobo, it's all running fine, it's just strange that since 0.9.1, I have never had a stable bitcoin app, that actually stayed 'running' like older versions did, kinda like start and forget, I was mining for 6 years constant up until 0.9.1, and since then, the problems are increasing, and the only time I've formatted in last 6 years was at the weekend, which I only did to start afresh, in order to check if my hard-disks were ok, they pass..
As for moving to a new OS, nah, I stopped upgrading when the icloud came along saving my work on others pc's, I thought, how will this affect my copywrite to my own work, if it's saved first on someone else's comp, as this means they own the intellectual right's due to them having the origional! So no more upgrading for me, I got 6tb of audio running fine on ye auld sp3, (shame about only being 3.odd gigs mem). Tbh, I found windows seven prevented the majority of audio apps I have from working in one way or another..
3rd attempt at starting, seems stable for now, but will it be running in the morning.. hmm..
It took 4 starts in order to actually start, and it died everytime it connected to the net, not that I think it's being disconnected, or blocked, but what if the p2p protocol was restricted (using data caps? - I dont have data caps, but the method would work) to the point that the app could not download the blockchain, even though it could 'see' it? it's like, downloading a movie at 0.01bytes a second, would this not time out the app? 
