Service stabilitrak,traction control ,and check engine light are on .

Hello, You have more than one issue with your DTS, one issue is that cylinder number 4 is not firing all the time, if ever, and the other is likely related to a wheel or vehicle speed sensor. Have the codes read again, and see if there are new codes in addition to the P0304 DTC. If no additional codes, as funny as it sounds, repairing the misfire (plug, wire, coil, leaky air intake, etc...) could clear the stabilitrak and TC lights. Let me know if you need more info!

Just change the alternator I had the same problem, changed the alternator all the lights went off immediately except the check engine light, that took like a day of driving and it eventually went off.