Maybe get a new card first then try the cable if you think it's good enough, no point in wasting money if you don't have to. Obviously main issue in your previous setup was poor card, even a great cable was unlikely to help such a crud signal.
Rex any recent GPU has solid and improve TMDS thanks mainly to the propagation of better panel, and the need to push resolutions at/near the max of the 165Mhz TMDS. And with the number of dual-TMDS integrated GPUs out there, go that route for future compliancy with higher resolutions and with the option for HDMI out.
Get a cable AFTER you've tested the new card if you still need one.
Some suggestions fro picture quality and good gaming performance;
Another thing to consider is that the ATi cards support 10bit per channel internally since the R9500 series, and the Geforce cards since the GF8400.
My recommendation would be you don't need a card that costs over $100, but if that's your budget, there's alot of sweet options there (despite my feeling AGP is a waste of money in general). But you could be fine with something in the $30 range that would blow away the FX5200. Funny thing is had you had a Radeon 9600SE at the time, or even R9100, you likely would've been fine.
Main thing is what you need to focus on? Cool & Quiet? Max Performance? Most importantly what's your power supply situation?
More than a big upgrade without a huge power supply requirement or much money;
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
A little cheaper and less power demanding;
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Unfortunately not many good nV options at NewEgg, the GF7600 is ok, but for the price and similar power draw might as well pick other options.
A nice quiet quality solution but needs bit more power too;
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Non-NewEgg there are other options too;
A little less power consuming than the HD3600, the 3450;
http://www.ewiz.com/detail.php?p=AS-3450AGP&c=pw
The thing about the HD series card from ATi be sure you read up on and prepare for the AGP hotfix if you plan on that route. If your motherboard is old, then older cards (like the Radeon 9600/X700 or GF6600) would work better on a 2X only mobo.
Problem with the higher nV cards, they're more expensive, so in AGP it's somewhat a one-side performance/value situation. A GF6200 would be an upgrade from FX6200, but not much of one if you're interested in gaming, and for the same price you can get an X1550 so it's a tough sell. Especially when both ATi and nV's recent integrated solutions would likely outperform and not only have good DVI support but also better oher overall features. So your money might be better spent elsewhere.
However if you prefer nV there's the GF6200, 6600, 7600GS, and then they start getting rare for things like the GF7800GS etc.