Trouble Starting

I have a '99 Monte Carlo, V6, 120k miles (car), ? Miles (engine). My mother blew the engine and my father had a different one put in, I'm not sure of the engines exact history.
The problem is when I try starting it "somtimes" it will start, though with obvious trouble. I had the starter rebuilt and it worked fine for approx. 2 days and it went back to acting the way it did. I can coax a start out of it once a day, "maybe" twice. Afterwards when I try the engine turns over a few times then stops- sometimes it won't even turn over. The turn over doesn't sound right, like its not fireing correctly. I checked the plugs and the look new (they should be since the engine was put in less than 500 miles ago), but my father- who is no car mechanic, thinks that its a combination of "needing a tune up" (sparkplugs mostly), and a starter.
Though I have a camaro that has a bad starter and the monte carlo's starter doesn't sound the same, like its going out, it dosen't "grind" (but then I'm no mechanic either). Any ideas would be a big help.