Your area is probably better than mine. I spent something like 4 months looking for my first car when I was 16 and foreign cars are extremely rare here, especially the $2-5k Honda or Toyota, because people would buy them up quick, privately at least, because dealers are way too expensive.
Anyway if you can get a Civic with < 100k for $4k I consider that pretty damn good. Cars like that, well any decent build car, that's mid 90s will run to 200k if its been taken care of. If you don't wanna get a < 1k beater (I can see why, you already got one, gotta upgrade a LITTLe eh

) then something that's about 3k will still be reliable. ANY car is gonna need repairs. I was pretty sad when I spent $400 a couple of times on my car, plus $200 for a distributor, plus all normal maintenance, so we'll say my $2500 car cost me another $1500-$2000 over 3 years. I could've just've well bought a $5k car and still have to plunk $1500 in repairs over the years.
I guess I'm rambling... I'm just suggesting to get something cheaper that you can almost buy outright. Research the car, have some savvy look at it before buying. I do believe there is quite a lot of < $3k cars out there that are reliable.
edit: Forget that advertising car, that sounds very schiesty. I don't know personally about police auctions but sometimes there's a reason things are so cheap. Look at the cars outside collission shops, yeah maybe its a 2000 for $5k, but the thing is prolly fvcked. Hit the newspapers and find a person or couple who can tell you something about their cars, whether or not they took care of it, changed the oil, etc.. The family I bought my car from was very nice and up front and by the ways its lasted, they took good care of it (I became the 2nd owner only, at 130k miles!).