I see the models PCG-TR2A and PCG-TR2AP frequently mentioned in conjunction with your model (even searches on Sony's site return them together) - try this one:
http://esupport.sony.com/US/perl/swu-download.pl?mdl=PCGTR2AP&upd_id=1002&os_id=7It's a driver for an Intel Pro/100 VE - it's a very common NIC so it's quite possible Sony used it in many of their laptops. If it is an Intel (likely), you can probably get away with downloading the "catchall" driver from Intel aka "PRO2KXP.exe". It seems Intel are having problems with their download center right now, but it's up on download.com
http://www.download.com/PRO2KXP-exe/3000-2112_4-196642.html