Couple thoughts:
First thing I would do is to remove the grease fitting, and clean out the cavity, and the back side of the fitting, removing any dried up grease. Might try soaking the fitting in solvent, then blowing same out with air. Then put the fitting on the grease gun, and see if grease goes through.
If all is OK with the fitting, or you have a new one ready, next, fill the cavity with as much penetrating oil, like PB blaster, or KROIL, as it will hold. Then re-install the fitting.
I have not had much luck with the hammer type uncloggers.
I cannot recommend this product highly enough:
http://locknlube.com/
Locknlube grease tip actually locks the gun hose to the fitting, if it can't get the grease flowing, you'll need to do some serious dis-assembly, to get any in there...