Arduino Ethernet shields use HW method to reset (initialize) the W5x00 chip. They have the W5x00's RST pin hard wired to Arduino's RST pin. If Arduino is reset, the W5x00 should be reset also. However ...

The reset pin may be configured as an input pin. But such configuration requires modification of Configuration Information byte, which require an external tool to do so.

One side of the capacitor connects to the DTR line of the USB-serial chip and the fourth pin from the left on the upper edge. The other side connects to the reset line which appears to be available ...