First off get one single cable that does what you want (ie. s-video to scart) in case any of those adapters are screwing things up.
Now - onto the more technical stuff.
First you need to be aware that the GeForce3 CAN NOT drive 2 displays at once so far as I know. I have a GeForce3 Ti200 and it can't anyway. So your choice is Monitor or TV - not both at once.
Having said that, it isn't detecting the TV in the first place so it's probably something more fundamental.
If you plug only the TV in and disconnect the monitor - what happens when you boot the computer? Does the BIOS status screen and the XP loading logo (assuming that's what you're using) appear on the TV? If it does, does it disappear/go garbled as soon as it gets to where the login screen should be? I have a very similar problem with my card you see.
It seems that nVidia fked up support for some of the rarer TV encoders they use on thier older cards, including the one used on my GeForce3. The only way I've found to get TV out to work (mine won't detect the TV either) is to use a program called TVTool which you can find here
Unfortunately you have to pay for the full version or it cuts out after 15 mins.
I wish there was a better way, but that is the best I've been able to find - and believe me I've looked enough.