It never rains but it pours.

Oooph. That's a rough situation. I'm really sorry. your mom is probably right though: if it's thrown a rod, and it's really old, it's ALMOST NEVER worth fixing.

If you were in the Northeast, I could get my dad on the case (he's a master auto tech, and works for a pretty large car dealership--more to the point, his dealership is full of Decent Souls who have been known to quietly set a nice little used car aside that would go to auction and let it go for a very reasonable price for people who really need it, and my Dad has been known to go through said cars and help cherry pick the best).

That not being an option, I've got a few suggestions that may or may not be useful, but I'll toss anything that might be useful out there. This is what I've learned as a mechanic's daughter and from five years working at a car dealership in college.

Someone else mentioned auto auctions. This is where a lot of trade-ins end up if the dealership doesn't want to sell them themselves. They will usually (but not always) pick the best to sell on site, and send the rest to auction. Sometimes they'll send away very nice cars, though, if there isn't room on the lot or if they don't have a lot of luck selling that particular make or model. If there is one in the area that allows the public, this can be a good option. They're What You See, What You Get, No Warranty, but you can find some nice cars there. I had a nice one at one point my dad pulled from the auction line. I got six good years out of it and it was a very reasonable price.

If you have a good relationship with a mechanic, it's totally worth asking if they will go through a car you want to buy before you commit to buying it and tell you what they think. My dad will do this for free for people he likes, but a lot of mechanics will do it for a very nominal sum for a good customer. Even private purchasers will often allow you to take a car for a small time to your mechanic. At least ask if you can, even if you can't (bluff if need be). If they balk and make excuses, I'd be VERY worried. If they assure you that will be fine, then you can rest a bit easier they're not trying to hide something serious.

Police cars tend to be sold very cheaply when they hit a certain mileage. This is a GREAT OPTION if you can find it. It's VERY HARD TO DO SO. Mechanics like to buy them. :) (at a certain point in my life I was convinced all mechanics had two cars: a decommissioned police interceptor and a Camero). If you happen to find some available (often at auction) don't ever go for the detective's cars, they tend to be beat to pieces. Go for the interceptors; they're rarely idled and almost always have most of their mileage on the highway. You want that: sitting in stop and go traffic is Death to Cars.

Old rental cars tend to be sold off the same way. This is more of a mixed bag. You see these at auto auctions.

Avoid late 1990s model Chevy Malibus. They tend to start developing break line leaks and they chew break pads like bubble gum. Not worth it. Malibus before that period and after that period are better bets,. I had a 1999, and it was Serious Trouble when it hit about 100,000 miles. the only reason it is still on the road (my brothers drive it now) is because my father is a master mechanic and he does a lot of work on it.

I have a Nissan Centra now and we really like it, for the record, and I have a friend who's got one that's from the late nineties and still runs well.

Look at the carfax (if you can) of where ANY car has been driven. Cars from areas which don't require heavy salting are to be preferred, all other things being equal. Salt is hell on cars. That's why you see more old cars in the south than you do in the northern states that get a lot of snow and ice.