It is very unlikely that all the pins are stuck. Is one pin different from the rest?
A spritz of CRC contact cleaner will do no harm. If a pin is stuck it may help free it - spritz and then work the defective pin up and down.
If all the pins look and act the same then the problem is more than likely elsewhere. Examine the little gold dots the pins make contact with - do they look clean?. Again a spritz of contact cleaner won't hurt.
If the problem persists the DP-20 may be broke, or the F4 may be broke. Do you have, or can borrow, another F4/DP-20 - it would let you isolate the problem to the body or the finder.