A GT240 only needs about 5 amps. The processor will pull about 10 amps. That doesn't leave much for the rest of the system.
Your PSU is an older one with a relatively light 19 amp 12 volt rail. In your case, it's not the power rating that is important, it's the 12 volt output. Your system will be running the 12 volt rail right at around 100% of capacity.
If you had something like the now discontinued Corsair 400CX with it's 30 amp 12 volt rail, I'd say, "No problem." Even the not quite as good 430CX (28 amps@ 12 volts) would do nicely.
Considering the combination of an old, obsolete, not particularly reliable design with a light 12 volt rail, I'd say that you should budget for a new PSU. A 400 -450 watt PSU will do, but it needs to be a good PSU.
The Coolermaster may be labeled to be able to just provide enough, but unfortunately that line of PSUs is overrated garbage, so it will blow chunks, possibly damaging other components. If the 650W Earthwatts seems excessive (despite the excellent price), for example if you will never install a beefier GPU for gaming, check out the 380W Earthwatts for $45 ($30 if you play the rebate game and win).