Well my battery died while I was out for the weekend(I'm guessing it was the alarm that drained the battery).[:@]
My brothers Pontiac Sunfire(Funny enough, same engine as the Cobalt, 2.2 Ecotec) attemps to jump me, well it makes the normal "Wer...Wer...Wer" sound you expect with a dry battery. We try again, but this time with my neighbors Dodge Ram 2500.
This time around, when I turn the key it makes a rapid "Click Click Click Click"
This kind of worried me, didn't try it again, and gave in a bought a new battery.

What was this "Click"ing sound?

Also, someone told me that it's actually dangerous to jump start cars, said it could burn the CPU or something, is that true?

 

The clicking sound is your car had enough battery to start your accesories but it does not have enough volts to start the car...its normal man dont stress it.

 

The clicking sound was fron the starter solenoid cycling open and closed due to there not being enough amperage available to keep the contacts closed.The "wer,wer" sound was the starter trying to crank the engine.It couldn't because there wasn't enough electrical power coming through the cables.
You should have tried to reposition the cables so they get a better connection to both batteries.Allowing a little time for the recieving battery to pick up a charge would have helped also.
Keep and eye on your alternator,they weren't designed to charge a dead battery,only to top off the battery after an engine start.To properly do this also takes time.It can take a half hour of driving to recharge a car's battery after a start.