Welcome, Belga. When the service stability system warning comes on, does it also disable the traction control and anti-lock brakes? if so, you could have a bad wheel speed sensor in one of the hubs, which could also cause problems with the tire pressure warning - although the stability system generally gets set first.
If the TC and ABS is not disabled, the most common cause is the steering position sensor. None of these codes will show up in a standard code reader. A Tech II scanner, or another capable of reading the ABS/TC is needed.
If you haven't already, try this for the tire pressure warning. Check to be certain that the pressure is equal (within a pound - two at most) in each tire. Then, on your DIC (digital information center) on your dash, press the select button until "Tire Pressure" is displayed, It will probably say low. Then hold the reset button until it resets, and shows normal. It could take about 5-7 seconds for this to happen.
Black 2000 SSEi, Silverstar Headlights, Angel Eyes fogs, 3rd brake light overlay, hi-flo cat, drilled 180 degree thermostat, Intense FWI, PCM, shift kit, and 3.4 Pulley. Solid front mount.