Welcome to JustAnswer.com! My name is DriveFast71(Ron) and I will do my best to answer all of your questions completely and accurately.
When the Check Engine light comes on, the Slip, VCS and Trac lights are also set. This is a self-preservation mechanism, that turns these systems off, in case the reason the engine light is on can harm or effect these systems. SO- fix the reason the Engine Light is on, and the other systems will come back online.
From what you are describing, it sounds very much like you have a "cylinder misfire". Very commonly on these engines is a faulty Ignition Coil. These coils sit atop the spark plugs, and send current to the plug, causing them to fire at the correct time. When one is faulty, iot does not send current, or not enough current, and you get the "shaking" symptom. This could also be the case of a faulty spark plug, or a clogged/faulty fuel injector. At this point, will need some Diagnostic Trouble Codes (aka "p-codes") to correctly determine if this is, in fact, a misfire, and if so- which cylinder. No need to replace all the ignition coils if the p-code reveals it is only one faulty one. (ie- P0304 would be a misfire on cylinder #4, and very commonly, the coil is the culprit). Most local "big chain" parts stores read these p-codes for Free (except in California). Once you have these p-codes you can more accurately and efficiently determine the root of the problem, and make the appropriate repair.