Howdy W38,
First of all I was letting my husband do the diagnosis.. that was part of the problem. When I went out and checked the battery contacts had much corrosion so we cleaned em' and it started right up. Drove it down to the smog inspection place and $147 later the car passed and all is now good.
To answer your question, yes I would keep it. It's basically a Toyota and they run forever... and it's much easier on the pocket to spend $1500 to keep it running then to have a car payment or buy another used car with unknown problems. $3000 is steep but if you trust your mechanic have him do a once over and get his opinion too.
Good Luck!!