bugs - a kind of problem that has something to do with computers or glitches
worked out - have we solved this problem or have we fixed the problem
tech guys - people who works on technical things like computers
more problems that they had bargained for - means they didn't think there will be so many problems and they found out later that there were more or you're expecting something and you got more than you have expected
ship shaped - everything is in order or everything's fixed
get on the horn - means telephone or call, imagine the telephone as some kind of a horn or call these people up
meltdown - a word for a really large problem or so many things have gone wrong
not footing the entire bill - means he's not going to pay the entire expenses for the computer problem
what you want to relay to them - means what you wanted to tell them
no uncertain terms - tell them directly or tell them exactly; no beating behind the bush
chip in - means you expect them to pay part of the cost
stone wall - something you cannot get through; you can't get beyond or you run into it and you stop, it also means that the people you're talking to does not agree to something that you wanted to do
patch them through - simply means to connect them to me on the phone, make them talk to me one on one
handle - deal with the situation
