A/c compressor not engaging 2008 caravan - 2008 Dodge Grand Caravan

You say refrigerant is "full", but it can have too much. If you have attempted to "top off" your refrigerant then you may have too much, keeping the compressor from engaging. If you haven't messed with it and the compressor just stopped engaging on it's own then I would start checking the relay, fuse and the ac switch.

1) TEST the fuse+ relar of a/c
see the next steps and fix it. God bless you
If so, the compressor is working and the A/C system probably contains enough refrigerant to make cold air, so the problem is inside the HVAC unit. Replace the motor that controls the blend air door (this is a difficult job and best left to a professional since it involves tearing apart the HVAC unit -- about an 8 to 10 hour job!).
If the compressor does not engage when you turn on the A/C, see if it will run by jumping the compressor clutch wire directly to the battery (use a fused jumper wire). If the compressor works when you jump it, and the A/C blows cold air, the system contains refrigerant and the fault is likely a bad A/C compressor clutch relay or a bad clutch cycling switch or pressure switch.
If the compressor does not engage when you jump it, the problem is a bad compressor clutch.
If the clutch engages but the compressor does not turn (the belt will start to slip and squeal), the compressor is locked up and you need a new compressor.
If the compressor clutch engages and turns the compressor, but the A/C still does not blow cold air, the system is probably low on refrigerant and needs to be recharged

on the back of the compressor on the larger suction line or in the larger suction line at a convenient place
the line that runs from the compressor back to the firewall

A have problem for my van 2008 caravan my problems is when start the a/c the fan do not aplicate the high velocity thank you for help

The r134a pressure may be low in the refrigerant lines causing the compressor to not engage as a safety measure for the compressor.

Check the belt alingment. Something could be in the belts pathway that is shredding your belt. Also check your compressor to make sure it is turning when the compressor clutch is engaged. If the clutch is engaging and the comprseeor is locking up it will burn the belt or snap it right off. Also check your tensioner pully and make sure it is free spinning.

DON'T TRY TO FIX THEM UNLESS IT IS THE CLUTCH ON THE PUMP THE CLUTCH COST ABOUT 80 TO 120 DOLLARS THE WHOLE PUMP WITH THE CLUTCH IS ABOUT 180 DOLLARS
THE NEW ' OR REMANUFACTURED UNIT WILL OUT LAST THE CAR ( AUTOZONE HAS THESE IN STOCK )

check fuel pump and relay, remove cap listen for whirling sound in tank, listen for click under hood for realy

U may be low in Freon gas.
When Freon is low there's low pressure switch that will prevent A/C compressor clutch from engaging to protect it from failure.
So, first check Freon pressure & any leaks form lines & hoses fittings.
Even if the fan is working, that doesn’t indicate proper compressor OP'S.
Look at the compressor front side you'll see the clutch stationary while the AFT pulley moving.

Then put air-condition compressor switch to ON (Engage),
You should see the clutch engage & start rotate,
If NOT, this is very clear indication u r low in Freon.

Regards;
MAR

First suggestion is the clutch not engaging. Check voltage at clutch plug and confirm power source, if there is power there then clutch would work unless it has failed.