Engine service light stays on and won't change gear

WOW YEA! I had a SIMILAR problem with my Chevy Malibu! That puppy DIED in a very busy California intersection! I mean the POLICE, a tow truck and trip to the auto mechanic who spent HOURS tracking down my problem.

At one point the mechanic was 80% SURE one of my COMPUTERS was bad! That is spelled with a $$$

The real problem?? The FUSE BLOCK got >>>wet from the BOTTOM<<< and drove my COMPUTERS NUTS until the Fuse Block was thoroughly dried out! And I do mean COMPUTERS because of the many 'fault codes' from many directions.

I mean the codes were serious enough to shut the car TOTALLY DOWN!

Later I got a sheet of rather thick plastic and made a shield to block any future car wash water and road water exposure. I mounted the "slightly extended plastic sheet" UNDER the fuse block to block all water from under the car... NO problems like that since.

Good luck!
Anthony

Disconnect the battery for 30 minutes. You will have to reset the radio/clock afterwards though.

there is possibly water in plugs and connections . Blow all areas with air and use a water dispersant(WD-40) to remove the water in the connections Run the scanner for the fault codes to reset the light.

ABS light coming on,For this get the Engine computer scanned.It can be error codes stored in computer.------------
For more details regarding this click the link below:-----
The ABS and Traction Control Lights stays ON dash of car? http://schematicsdiagram.blogspot.com/2011/06/abs-and-traction-control-lights-stays.html

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And now for clutch not going in gears it can be faulty clutch issue or problem with clutch cable.This has to be inspected.For more detailed instructions regarding Peugeot clutch problem,click the link below:-----
Peugeot 307: Clutch will no go in gears?
http://whoisbyme.blogspot.in/2012/05/peugeot-307-clutch-will-no-go-in-gears.html

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This will help.
Thanks.

it has trouble, you will need to get it scanned for the engine light. Never wash an engine.

CHECK ENGINE light??? Whenever the 'CHECK ENGINE' (Service Engine Soon) light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on.
You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE the problem and perhaps eventually fix the problem.

Yeah... why did you change the MAF?... Someone tell you the MAF caused your transmission to shift from 5th to 3rd?... I don't think so!
Did the 'Check Engine' Light come ON? Whenever the 'CHECK ENGINE' light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on. You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE and perhaps eventually fix the problem.

change speed sesor or shift solenoid.

DTC P0734 is "4th gear incorrect ratio" - that's your torque converter 'LOCK UP Clutch" It's worn out (or you're using the wrong Trans Fluid required by Hyundai - SPIII OR Both). The P1624 is simply the Trans Control Unit (computer) communicating to the Engine Control Module (ECM computer) MIL - on request signal to ECM = asking it to turn on "Check Engine" light. MIL = Malfunction Indicator Lamp. When the torque converter 'lock up" clutch slips or doesn't engage, the trans automatically returns to 3rd gear and stays there (it's called 'fail safe' mode) until you cycle the ignition key, then everything resets until the malfunction occurs again.
You'll need to have an AT (Automatic Transaxel) tester hooked up to verify this. Hyundai has a Service Bulletin specifically for "gear incorrect ratio' codes. If when you changed the trans fluid, was it done at a Hyundai Service Center? If not, someone may have installed the wrong fluid.

I had the same problem--turned out there's a switch on the steering column behind the steering wheel. You've probably found it by now, but wanted to share :)