This is odd. What are your Network Adaptor and PS2 models? What is the maximum speed supported by those devices that the both of you connected your PS2 to?
The SCPH-10190 PCMCIA network adaptor of my SCPH-10000 refuses to work properly at all with any 1Gbit network devices, and automatic negotiation fails (After a loooooooong time).
I don't know about the SCPH-10350 network adaptor, as I use a SCPH-10281 with my SCPH-39006 console.
Unmodified SCPH-77006 with SM 3.6
SCPH-39006 with M-chip modchip, SCPH-10281 NA and refurb Seagate 80GB HDD
SCPH-10000 v1.00 with SCPH-10190 PCMCIA NA and SCPH-20400 HDD unit