Diagnosis
A leak from the pump housing at rest means a seal has failed. On the K1700, the most common leak point is the inlet water seal (where the water enters the pump) or one of the shaft seals on the piston assembly.
How to Fix It
Since it leaks with just the water supply on, it's likely the inlet seal. You'll need to disassemble the pump head. Unplug the machine, disconnect the hoses, and remove the four bolts holding the black plastic pump cover/head. You'll see the water inlet passage. The small rubber O-ring or flat seal in there is probably cracked or deformed. Replace it with a new one from a Karcher service kit.
If That Didn't Work
If the leak persists from the same area after replacing the inlet seal, the pump head itself might have a hairline crack, which is less common but can happen if it froze with water inside. Inspect the plastic carefully.
Heads Up
Always store the pressure washer indoors or in a frost-free place. Water left inside can freeze, expand, and crack plastic housings or damage seals, which is a guaranteed leak.