Best bet may be to replace it with another 6200 low-profile card, then. There are other low-profile AGP cards available, like the 4350 or 4550 from ATI. These should also work, as their peak power requirement is actually less than a 6200's. The trouble is finding them...
This chart I'm about to link can be confusing if you don't know your card generations, but I'm linking it anyway. It separates them based on brand and generation. Just find the 6200, which is around 20 up from the very bottom, then try to find other cards with about the same wattage ratings.http://mark.zoomcities.com/images/gfx/GFXpowerchartbybrandgen.png
You'll see that the ATI cards I mentioned are in it's league, as are several others. However, due to their age, many of these cards are no longer available. Here is a link to all the low-profile, AGP cards Newegg.com has to offer:http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=2010380048+1069609639&QksAutoSuggestion=&ShowDeactivatedMark=False&Configurator=&Subcategory=48&description=&Ntk=&CFG=&SpeTabStoreType=&srchInDesc=low-profile
You may find others available elsewhere.