I've encountered this before on my old Jetta as well as some of my friends' cars. Both of these systems work using a signal from wheel speed sensors that are generally mounted on or near the brakes. They're usually about the size of a roll of pennies. If they're gooped up, bent out of alignment, unplugged or the wires are damaged they will send a "no-spin" signal to the computer, telling it to activate the ABS (that pulsing you're feeling in the brake pedal) as well as cause all sorts of errors in the traction control module. That seems to be the most likely source of failure.
If you determine that one or more of the sensors are faulty, check your local auto parts store for replacements or rockauto.com. The dealer should be your last resort buying parts since they mark up their parts 100-500%.
Fixing the sensor(s) may not make the lights go away. You'll have to take it to an authorized GM repair shop or dealer to have them reset the computer modules for the ABS and TC.
OR, if you're feeling wealthy, you can buy one of those nifty gadgets yourself, but be warned: the ones that can access ALL the computer's modules cost $$$$$$$$$$ (those $200 OBD-II units at your local auto parts store can only access the engine module) and require you to get a hold of some good factory literature so that you don't change a setting that will break your car even further. Best of luck!