Need to know what year vehicle. OBD I, you can jump to read codes, OBD II, you can't. The change was made in 1997 I think.
Transmission jumping hard is the malfunction causing check engine light to come on,most likely its the tcc solonoid causing this or a possibility of causing this.
As previously said. Dead, or weak battery. The light you're talking about is a blinker signal light, not a check engine light. It's just coincidental.
If you have plenty of power in your battery to start your engine and everything seems fine except for the check engine light, try disconnecting your (red) positive battery cable for 5 minutes and then reconnect it and see if this reboots your computer. If the check engine light does not go off then, have a mechanic look at it.
Check engine light should have an Error code,ask mechanic to read it for you. then he will be able to expalin to you what is the reasona nd the solution for this.
Check engine lights can come on for a number of reasons. If you didn't get the cable right or got a sparks when connecting or disconnecting that could most definitely cause problems with the check engine light or even blow the alternator fuse.
5S-FE engine. engine warm. jump terminals TE1 and E1 in the data link collector box in the bay. hook up the t-light, timing is 10 degrees BTDC
Check that engine mounts aren't broken.
clicking sound but engine wont turn over. jump across terminals on starter if engine turns over solenoid is bad.
I would check the battery terminals, probably a buildup of corrosion between the posts and the terminals, clean them up with boiling water and sandpaper till both parts are shiny clean. If you are connecting the jumper leads to the battery terminals when jump starting and it works fine then this is the only possibility.
Check the engine RPM. If the engine is running too fast when you put it into drive, it will cause the vehicle to jump.
jump terminal on the driver side with the blue-green wire and the brown wire then start engine and using the light gun check for tdc at a tolerance of 15 degrees
Get a 10mm socket and just take the terminals off, put in the new battery and reattach the terminals. Feel free to jump over to Smokinvette.com and check out the C6 technical section to get full details on this.