Take the PS2 apart, unmount the mobo from the case, disconnecting the fan, the two flatcables which go to the DVD drive mechanism and the flatcable which goes to the HDD bay.
With the motherboard assembly out of the case, take out the top EMI shield ( 4 small screws. That's where most of the fuses are at.
Top of the small board:
PS407 CCP2E50 (marked as "50") HDD 5v ?
Check too PS410 on the top board...
On the big board check all fuses marked as "50"
Since the network adapter works fine online it's very likely one of these fuses blew. Any doubts you have, take it to a electronics technician. Even those who fix soundsystems know how to replace these fuses.
SCPH-10000_GH-001 SCPH-15000_GH-003 SCPH-18000_GH-008 SCPH-30001_GH-005 SCPH-30000_GH-016(V4) SCPH-30001_GH-010(V4)
2xSCPH-10190, 2xSCPH-10350, 2xSCPH-10280
"**** j0 hackers!"
-Sjeep (As seen on TOXIC OS ELF...)