How do I make my Sony notebook model PCG-9G1L compatible with modern ethernet cable connection?

Try here: http://www.laptoppartsexpert.com/c-49829-sony-vaio-pcg-9g1l-notebook-repair-parts-accessories.html or ebay

It seems like you need to reinstall the modem drivers from the CD or download them from the internet.

first there should be 2 cables connected the device.
1) power adapter
2) ethernet cable from either a dsl modem or a cable modem connected to the wan connector
with most cable modem service its usually dhcp meaning you are always connected to the internet
with some there is ppoe connection where a user name and password is used to make a connection to be on the internet with the dsl modem
there are some dsl companies that are dhcp just like the cable modem companies.
with the ethernet cable connected the wan port on your router there should be some kind of activity light on the router but check with the type connection from your dsl or cable internet provider. also you will need a second ethernet cable to connect your computer to setup and configure the wireless settings and wep protection.
need more info?

You can download the device drivers from the Sony WEB site.
Select your model notebook and the Windows drivers you require. Pleaseclick on this link to the Sony support WEB site :-
http://esupport.sony.com/US/perl/select-system.pl?PRODTYPE=1,24,72&DIRECTOR=DRIVER

Any "modern" notebook computer will have both an Ethernet adapter and a wireless adapter built-in, especially one labelled as a "business" model.

Click Start
Click Control Panel
Click Classic View
Click System
Click Hardware
Click Device Manager
Click the '+' in front of Network Adapters
to show the installed adapters.

Take an Ethernet cable, and connect one end to the Ethernet slot in your computer, and the other end to a cable-modem or a DSL-modem, and you'll have an Internet connection, through the Internet Service Provider of your choice (Comcast, Roadrunner, Verizon, et cetera).

Or, connect "wirelessly" at the local Starbucks.

yes and it is mostly located at the back

go to device manager and check its type then try to install it.

Here is the Service Manual for you, hope it helps you.

Did your sony vaio came with a cd installer? If it has one, you can use that to reinstall the ethernet controller.

Hey MIDO Try This Tool

VAIO Launcher 1.4.11 Update Program

This program will update VAIO Launcher pre-installed on the VAIO model listed below.

VGN-S4HP/B
VGN-S4HRP/B
VGN-S4M/S
VGN-S4XRP/B
VGN-S4Z/S
VGC-V3S
VGC-V3M
VGN-FS285H
VGN-A497XP
VGN-A417M
VGN-A417S
VGN-FS295XP
VGN-FS215Z
VGN-FS215M
VGN-FS295VP
VGN-FS215B
VGN-FS215E
VGN-FS215SR
VGN-FS215MR
VGN-FS285M
VGN-FS285B
VGN-FS285E
VGN-FS215S
VGN-B3XP
VGN-B3VP
VGN-S4XP/B
VGN-S4VP/B
PCG-K415S
PCG-K415B
VGN-FS195XP
VGN-FS195VP
VGN-FS115S
VGN-FS115Z
VGN-FS115M
VGN-FS115E
VGN-FS115B
VGN-FS115ZR
VGN-FS115M -- ( Thats Ur MODEL)
VGN-A397XP
VGN-A317S
VGN-A317M
VGN-S3XP
VGN-T2XP/L
VGN-T2XP/S
VGN-T2XRP/S
VGN-S3VP
VGN-S3HP
VGC-RA304
VGC-RA204
PCV-RS704
PCV-RS702
VGC-M1
VGC-V2S
VGC-V2M
VGN-T1XP/L
VGN-T1XP/T
VGN-B1XP
VGN-B1VP
VGN-S2XP
VGN-S2VP
VGN-S2HP
VGN-S2XRP
VGN-S2HRP
VGN-A297XP
VGN-A295HP
VGN-A217S
VGN-A217M
VGN-A215M
VGN-A215Z
PCG-K315Z
PCG-K315S
PCG-K315B
PCG-K315M
This update resolves the problem of registered applications not launching from the VAIO Launcher toolbar.
Note: This program requires VAIO Zone 1.2.05 or later. If your VAIO model comes with VAIO Zone 1.2.02, you must first update VAIO Zone before running this program.
Download and installation
1. Download the file SOAVZN-01028300-UN.exe and save it to a download directory
2. Close all running applications
3. Go to the download directory and double-click SOAVZN-01028300-UN.exe
4. The InstallShield wizard starts
5. Click Next and wait while setup is installing the new software
6. Click Finish when the installation is complete

HERE