getting sufficient current to your starter (more likely), or your starter is going bad (less likely).

I'd start with assuming your starter is good and eliminate any potential cable/ground issues by checking all of your cables and clamps and cleaning off any corrosion. Get a wire brush or terminal cleaner and clean up all your connections so that they look factory new. Then try jump starting it again. Even if your battery is bad, you should be able to jump start it.

My best guess is that you have a bad battery (which is why your car won't start on its own) and corroded terminals (which is why you're having a problem jump starting the car). As Bert pointed out, you could have a bad/corroded/loose ground as well.