I hate to be the bearer of bad news, but if there is smoke coming out of any electronic sub-assembly it is too late to worry about stopping it smoking. You are already thinking about repair / replacement.
If this work station belongs to a company - ie not your personal property - pass it rapidly into the hands of IT. Among many other things, that is what they get paid for.
If it is your personal property, then things get harder. PCGeek has a good point. Pull the PSU and the video card and have a good sniff at both. The PSU is a sealed unit and virtually non-repairable. If it smells of smoke or burning, or shows signs of soot or smoke marking around the air out vents, it is a very safe bet that it is toast and the only practical action is replacement. However any competent electronic shop can test it further.
If the video card smells of smoke or shows signs of scorching, repair may be a possibility. I had a quick look on Google for this card and saw a price on Newegg that made my eyes water - just under £UK 4,000. c$US 5,000 ? At this level of money I would be on the phone to nVidia's service department seeking help. You don't say how old this card is, but if the PSU tests good you may have a warranty claim. Failing that, a claim on your insurance ?
This doesn't do anything for the inconvenience of not having this system available, and I presume you didn't buy / build it to get 'Floppy birds' to run faster. If examination does show that it was the video card that was smoking I think nVidia is your best bet. Give them a ring.