Transmission going into limp mode. Have changed fluid and filter, went 300 miles and back to limp mode. Had a gas cap that wasn't the correct one so I just bought a new one. getting codes po456, 442, po700, p1776. any suggestions?

I assume Automatic Transmission?
Today's Cars are very particular about correct CLEAN fluids
AND filters!

"ATF" in most cases means Automatic Transmission FORD
Someone has done a transmission service with FORD transmission fluid.

The damage is done, there is nothing I can do for you.

However, you can try flushing the system of ATF with Dextron III
Automatic Transmission fluid at a Oil service company.
This will flush all the Damaged parts through your already damaged Transmission into the filter, doing further damage to seals and... along the way. Plus change the Transmission filter.

Bottom line;
Regardless of correct Fluid, The Transmission fluid IS dirty,
The Transmission needs clean Fluid and filter changed to run correctly, In any case; This may save what ever is remaining of your Transmission's life or not and your Car won't move at all.
OR you could do nothing and the Car May run another 30,000 miles or another 300 miles.

IF after doing a Transmission service the car won't move,
you can try putting the FORD Transmission Fluid in, which is an old trick to TEMPORARILY fix old worn out Chevy Transmissions.

Your Choice :)

I suggest playing the Slots at a local Casino first, to see how your luck is going before making a decision.
GOOD LUCK!

Not enough information to go by, so for starters, check the transmission fluid level, check for engine code(s), check for defective O2 sensors, check for defective catalytic converter, check for blown/missing fuse for transmission, check for defective transmission switch. When was the last time the vehicle had a tune up? Was the vehicle serviced, how recent (might have a loose connector)? Is the gas cap serviceable? These would be where I would start looking, then worse-case-scenario might be a bad transmission. Otherwise, the information given indicates that the vehicle went into limp mode.

Many of todays cars have a mode called Limp Mode. The Motor and Computer talk to each other and if faults are found? The Limp Mode (( Short for Limp on home mode )) will be set in the Computer. Go to your local Auto Zone and ask them to Scan the OBD 2 fault codes with their reader. Or pay the dealer. It may be something really simple. My Check Engine light was on the other day because the Gas Cap was loose. This Scanner told us the problem and we tightened the Gas Cap. After 3 times driving the car with it tight .... The Check Engine light went off.

have a pressure test done on the box to check for internal faults. Any high pressure leaks will cause heat. check the filter and while the pan is off adjust the bands and clutch packs . Check the radiator cores are not blocked as engine temperature will affect the transmission oil temperature . check oil level as extra oil will cause frothing and over heating.

this can be from a couple of things....fill it with gas drive it for 5 miles. replace the gas cap! the last thig is that the trans need rebuilding; the seals are not working properly and will not allow the fluid to flow which does not allow for proper shifting. i changed fluid and trans filter but only got 600 mile before I had to rebuild it $1300.00

PO456 is most times a gas cap or gasket,
to get an incorrect gear ratio the transmission has probably started to slip.

Change the fluid and filter first off in the transmission and use only atf+4 fluid and possibly the govenor pressure sensor,and change gas cap.

limp mode as in computer limp in mode?check the trans fluid is it dark looking?, Need more info. Did you have the trans fluid changed recently? The reason i ask is when you change the trans fluid way after its do the new trans fluid is detergent type and fresh fluid can put the transmission in shock(Trans Shock). This can wipe out a transmission in 5 miles or so seen it too many times. Let me know how it goes. Lee

the car has the capablilites to give data and codes. You gunna need a professional if you dont have access to a scanner and multimeter. Otherwise were just guessing.
I hate telling people that its out of their hands but sometimes its best to let the pro diag it and then you can repair it if you capable

Check the transmission fluid level and condition of the fluid. It should be bright red like Strawberry colour. If it's dark like burgundy, then the fluid is burnt and the transmission needs to be serviced. Fluid and filter changed.
Have the Truck's computer scanned for any DTC codes. Most parts store like Auto Zone or Parts Source will scan for free. If there is a engine management Issues, it may be running your Yukon on a limp mode.
Limp mode will not let the transmission shift past 3rd gear and the OD does not engage, i had a cracked ignition cap and the computer put me on a limp mode once. 
Good luck and hope this helps. Keep me posted to please.

Flush out your transmission with the correct type fluid, Mopar ATF+4, and correct filter. Disconnect Negative cable, to reset computer, for at least 24 hours. Check grounding straps for PCM, ensure they are tight and clean.
This method worked on my 2003 Intrepid SE, 3.5L, Police Pkg car.
Good Luck!!