Linksys WAG120N - Terrible Signal Strength?

linksys worse than thomson? that's odd
anyway, have you tried changing the channel? since many stuff can be interfering with the signal, e.g cordless phones, especially if it is a channel 6, which is the default channel for many wireless devices, plus, check what is the most common channel for your neighbors' wif's and make sure you are not on the same one (i recommend http://www.softpedia.com/get/Network-Tools/Network-Monitoring/NetStumbler.shtml << this tool for the job. make sure you have the latest drivers and firmware, and if nothing works, change your antenna!

Linksys is known for having bad WiFi signal because it doesn't have an external antenna it has 2 small pieces of metal inside the casing which gives the signal. Thomsons have that big white antenna behind them (Mostly all wireless routers/modems do) which makes them have such good range.
What you can do is the following.
-Make a tinfoil antenna and place it on the sides of the thing.
-Try different channels as khalil13 has suggested
-Get wireless N adapters and get a hold of that technology (Better range , and a lot more faster in transmitting data)
-Put tinfoil under the router to reflect the signals of the antennas.
-Use your old Thomson as a dedicated WiFi router.

Well as Avo said, you can use your old Thompson as a Wifi router; though this means you have to run a CAT5 cable between the 2 routers. Or, you can get this: TPLink TD-W8901G ADSL2+ Wireless G 4 Ports Router

Pc and Parts has it. I got this router and have been happy with it ever since.

try changing the wifi channels