Hey EM,
I see that you've checked the cables, but it's the only thing that I can think of.....
Can you describe how you've hooked up the cables???
+ (other car) to + (your car)
- (other car) to ground /bolt/metal (your car)
Also check to see that you have the alligator clips on clean contact points / connectors....if there's any corrosion, make sure to wipe it off. If you're using a bolt or nut (from your vehicle) that has paint on it as your ground, you might want to take some of the paint off so that it's completely metal to metal.
...If you have an automatic, sometimes the car won't start if you don't have it in PARK (P) all the way.
Good luck! Let us know what happens.
Hopefully, someone else can chime in with other ideas for you!