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The only sure way is opening the side of the computer and reading the specs off the label, hopefully they put the label on the side where you can read it without removing the power supply and turning it around. While the wattage is important, the amperage on the 12volt rail(s) is also very important as far as the graphics card is concerned. What happens is that many less expensive power supplies split the 12volt outputs into 2 or more 'rails' and each of these rails carry a portion of the available power (amperage) to the motherboard and accessories. The two highest users of the 12 volt power is the CPU and the graphics card so the power from one rail will be supplied to the CPU through the 4pin (or sometimes 8 pin) connector that plugs in near the CPU and the other 12volt rail supplies power to the graphics card through the 20 or 24 pin connector (other pins on this connector will power through to other parts of the board as well). IF you have two say 10 amp rails (12 volt) your one rail may have more than needed to power your CPU and some other parts and accessories but the other rail may not by itself have enough available power to feed the graphics card and some other parts and other accessories during peak loads. When this occurs your graphics may pause due to power starvation and this is the lag you are experiencing. This is not uncommon when upgrading graphics while still using the original power supply.
If you do determine that you need a new power supply, avoid the really cheap models, look for at least 100Watts MORE than what you have (probably 400-500Watts) with one single 12volt rail (so you can use all available power as needed), and 80% efficiency rated or better. You will find that there is little difference in price between 400, 500, and even 600 Watts, but a larger difference in quality and efficiency so purchase one that will power your next upgrade as well. Also look carefully at the listed connectors to make sure you have all of what you need.
You have to be a little bit crazy to keep you from going insane.