Ok, as I understand from what you are writing is that you are a little bit confused.
Try the following:
1. In order to connect the PS2 HDD with the PC you have to change the jumper clip to Slave. Then change the jumper clip on the primary disc (HDD with Operating System) to Master. Connect them on the same cable. On top the Master and in the middle the Slave.
Turn on the PC and the system should boot.
2.Use the WinHIIP
to transfer the games on the PS2 HDD.
3.Turn off the PC disconnect the PS2 HDD and change the jumper to Master and connect it on the Network Adapter.
B.T.W. What do you mean that your PS2 is: unmodded fat1