Ok, here are things it could be . . .
First, the post is the part on the keg that that connector gets attached to.
It could be the beer out (black) connector. Since you switched that to the other keg and got beer out, it's not that.
It could be the dip tube, but you say you pulled that and cleaned it. It may have immediately got clogged again though. To test for sure, put the keg in a bucket and release the pressure, remove the beer out post but leave the dip tube in. SLOWLY put pressure back on and see if beer flows out of the dip tube (this is why it is in the bucket). If there is enough crud in the bottom of the keg it could be getting plugged up again.
Assuming beer flows freely, it could be the poppet. Clean out the post and make sure that the poppet moves freely. Since you pressed it down and got sprayed it might be fine, but it's worth checking again.
If it's none of those, then it might be the interface between the connector and the post. I think the easiest way to check this is to swap the post/poppet from your good keg to the bad keg and see if that fixes the problem. If the poppet is the wrong size for that keg/post then it may be that the spring in the connector is not strong enough to depress the spring in the poppet so you get no/slow beer.
I know you've said you've used this one before with no problems, but sometimes when you take kegs apart parts get swapped accidentally and that can lead to problems.