Even though I'm working on a set of space combat rules that will be sold for money, I don't mind directing you to free games, even those on the subject of starship battles.
quick-start rules for Ultra Starfire, published these days by Starfire Design Studio. However, I remember when Starfire first came out from Task Force Games.
It's a fairly straightforward ruleset--each ship has a single line of stats, with damage affecting systems linearly, so you have to destroy a ship's shields before you can hit its weapons, its weapons before its armor, etc. Kinda simple, but there's room for a lot of variety. And hey, you can try the rules out for free, so why not?
Anyone else remember playing this game back in the day?