Any reliable, smaller,used reliable vehicles available for $5-6,000 for elderly mom whose Horizon not running?

My mom has had a Plymouth Horizon --18 years old. The last couple years she has had problems with it where it can be hard to start or is just plain dead. We have taken it to 3 different mechanics(starting to lose faith there) & none of the mechanics can find anything wrong with it. We even took it to a auto electrical place that had it for several days checking the electrical system. Nothing found. All said my mom doesn't drive it enough. It should be driven on a long trip & this would probably take care of the "dead" when she tries to start it or sluggish starting. Have a hard time believing that she is the only one that doesn't drive her car every day long distances & has a dead car because of it... Only has about 23,000miles on it. She just had a tune up, fuel filter changed, engine sensor changed. She can only afford $5-6,000 for another used car. Anyone have any suggestions? Any cars no bigger than hers around that are reliable in that price range or is she out of luck