Internet issues

I'm having problems with the internet in my new apartment. For some reason my computer does not like Verizon. Anyone have any ideas? My computer says it has excellent strength when I use my wireless....But it's lying because I still can't access the net. When I plug directly into the modem, my computer says it's not plugged into anything. When I steel my neighbors internet signal [that's very low] I can access the internet fine, I just get booted off every 5 minutes. Is there something about Verizon internet that isn't compatible with some computers? Anyone...Ughh...Pretty much untill I get this fixed I will not be on that much