My vehicle will not go into park what would be stopping this?

What , make , model an year vehicle ?

Shift cable is broken or out of adjustment

Year/make/model?? The park brake is not designed to stop the vehicle. If it is working properly, you should be able to apply the park brake and put the vehicle in drive and it should not move forward. If the vehicle moves forward, most likely an adjustment is needed. With vehicle info, I can supply no help on adjustment procedures

Had this happen on 2 separate Ford Explorers. On one the problem was solved by simply pushing on the vehicle and rolling it about 8" until it locked into park. Had to do this a few times when stopped on level ground and the vehicle had not actually clicked into park. Then mysteriously the problem went away.

On the second vehicle the device in the steering column that actuates the little stop had to be replaced. We did go ahead and replace the brake pedal switch at the same time just as a precaution. On this Explorer the driver had broken the stop by forcing the shifter out of park. This caused the replacement to be slightly more difficult.

Quite often that will happen when vehicle parked with wheels turned, and/or vehicle on a slope, so try to avoid that in future.If nothing else, when parked on a slope, stop, keep foot on brake pedal, apply parking brake, put transmission in neutral, then take foot off brake pedal and wait for parking brake to stop vehicle rolling, then shift it into park. When leaving, put foot on brake pedal, shift to drive or reverse whatever direction your going, then release parking brake. Sounds like a lot to remember but you won't have to pull hard on shifter as before, and it could save a lot of money on transmission repairs down the road. Always try to park with wheels straight as well.
Now, with that said, if you parked with wheels turned, try hard to turn steering wheel in same direction wheels are turning, just slightly, as you try to turn key. Sometimes a quick yank in that direction will do it. Also make sure shifter is all the way in park before you try it. If your on a slope try rocking vehicle slightly up slope as you push/pull shift lever in to park and try to turn key at same time. If no luck, try pushing brake pedal real hard and try to turn key. Let me know how it goes.

there are a few things that make this happen but lets try this test...

NOTE... you must do this in a safe PRIVATE location!!!

stop the vehicle pointing down a slight downgrade, like a driveway, place the vehicle in neutral and turn off the engine.
then with your foot on the brake, release pressure and let the vehicle start to roll downhill. While rolling see if you can get the vehicle into park

REMEMBER...you need to make sure you find a safe place to do this. Avoid public places

also REMEMBER, you will lose the power assist of the brakes after your first attempt so be prepared to apply a lot of pressure to get the vehicle to stop

if you are able to obtain park in this test then you might have a bent parking pawl

if not... update us ASAP

It is known as the Parking Pawl assembly, and requires removal of the gearbox from the vehicle along with the transfer box. You then remove the extension housing (requiring new bolts) and then replace the park lock gear and o'ring.

Are you saying that the car did not stop when you applied the brakes?
A vehicle does not automatically go into park when the brakes are applied. You have to manually put the vehicle in park with the shift lever.
If your car is not STOPPING when you apply the brakes - then this is a serious problem with the BRAKES!

That would be your neutral park switch is bad or broken. If the shifter linkage is not aligned with the neutral park switch it will not work properly. Located on drivers side on top of Trans.