Just to sum things up from my perspective, I would recommend the following:
1. First and foremost, buy a new PS1 SCART cable. As others have said, it sounds like yours is wired for composite instead of RGB. It is not that expensive and will be much easier than trying to fix your cable.
2. Don't buy a Sync Strike if you aren't going to get a scaler of some kind. The Sync Strike is going to output a 15khz RGB signal that most modern displays won't recognize on their VGA ports. I didn't need a scaler because I am using an older CRT that can handle 15khz (this was the source of my earlier confusion and bad advice - sorry about that)
3. If the new PS1 SCART cable does not improve the image then you are out of luck on the RGB front unless you are willing invest in a scaling solution. Here is a rundown on some popular scalers
If the new PS1 SCART improves the image but the sync signal appears to be off then a sync cleaner is needed. You could build one into your SCART cable if you handy with a soldering iron
http://www.mmmonkey.co.uk/composite-syn ... er-lm1881/ The LM1881 is the same device used in the Sync Strike for cleaning the sync signal.
4. If the new PS1 cable did not improve things and you still don't want to invest in a scaler, then I'd say a decent s-video to SCART adapter will be the best value for your money. A good s-video to component/hdmi converter will be expensive and you'd be better off spending your money on a scaler.
5. Another option would be finding a old CRT TV locally that accepts RGB via BNC or SCART. If you are patient, they can be had for very little money. I got mine for $50.
I hope this clears things up and does not add to the confusion that I caused earlier.