2003 Buick Century intermittent starting trouble

In the last 2 days my car started up fine and ran fine until I shut it off. When I tried to start it one minute later it started up but was running with a very weak, thready idle and quit entirely after about 5 seconds. After that it would turn over fine and seem to be on the verge of starting but not fully catch. During both instances I left the car for alone for over an hour after it failed to start. An hour later, it started up as if nothing were wrong. And it started up several times after that.

Late last winter, it failed to start after I left it for 10 minutes. It sounded like it was on the verge of catching but no dice. It was towed to a garage and the next day it started right up. They did a tune up on it, but obviously this problem is something else entirely. Last spring, after being shut off for 2 hours I couldn't start the car and was going to make arrangements for a garage to pick it up, but after an hour I got it going and it was fine after that?