Like Slippy mentioned, DK is notorious for locking up on diagonals until you center your stick -- it is not a good game to test whether your stick/switches/wiring are actually working or not.
If you insist on using gameplay to test your stick, choose an 8-way game
or change the restrictor to the plus/cloverleaf
and choose a 4-way game that doesn't lock up when you accidently hit diagonals.
BTW, you can fine tune the Zippyy by
carefully bending the lever arms like
this.

Green zone = OK to bend
Red zone = Avoid bending
Have you tried either a keyboard tester like the one packaged with
KADE Loader or the gamepad tester in Windows? (not sure which style of encoder you are using

)
If the keyboard tester or gamepad tester doesn't register joystick presses properly, you may need to do continuity checks with a multimeter to ensure that you have good microswitches and solid mechanical (wiggle wires and look for continuity to be broken) and electrical connections in the harness?
If the microswitches are bad, consider getting the LS-32 switch upgrade kit from
Paradise Arcade Shop. (great product, use them in all my Zippyy and Happ Super sticks

)
If your crimps are bad, Paradise has pre-fab daisy chains and rainbow packs of pre-crimped wires.
Scott