That is typical story, I have had about the same here with ours.
I didn't mean them, I meant an actual company that deals with this stuff, a professional, like a 'Pest Control Company', not a city worker that doesn't take his (hourly) job serious enough.
(Actually, here, we have Animal Control Officers, which look like the Police, (with guns) they take down your complaint and then do nothing I guess.
The reason I say that is, I have called over 15 times to our Animal Control, they say they can't find the neighbor dog in question that I called about which is barking constantly, and I do mean constantly. I guess now I will just have to call the Police and see what they do, calling them enough 'should' help them decide to make the Animal Control do something about it all.
A few years back I had MANY, MANY (11) feral cats in my backyard, I called ALL of the places that were supposed to help, but they were all full of feral cats and dogs, so I was left with nothing, I had to fend for myself.
What I ended up doing was trapping the cats my self with a (actually 3) cages that were exactly what the City uses, I got them for $17.00 at Harbor Freight. (After your problem's solved, you can sell these at a reduced rate on Craigslist if you want, I gave mine away to a neighbor)
I placed them in 3 areas in my backyard with cat food, and waited, it took them a while to trust the new 'thing' in the yard, but eventually I got a couple. I had also worked out a deal with a 'No Kill' place that helped me find a Vet that would spay and neuter them for a small price, so I took the cats there then released them. Now I had to catch the others, it was HARD to do, the amount of frustration in this was crazy, but it had to be done.
Anyway, this has nothing at all to do with your problem, but this was a very had, And VERY EXPENSIVE thing for us to do, it cost us several hundred dollars before it was all said and done.
So, I can kind'a relate, kind'a... 
I looked on YouTube to see if there was anything at all there, I found this...
http://www.youtube.com/watch?v=YKPNmKnm9Ro
(These traps are identical to what I used on my cat problem...)
Be sure to look at ALL of the videos that apply, you are not the first, or last to have this problem, there is a good way, it's up to you to decide which is best for your problem.
Good luck with that though, I am SURE you'll need it! 
Randy