No it won't
You will need 150w alone for the 370. That's too much for the psu to run the system stable. The 12v rail of the psu just have 14A max., the gpu uses 12.5 max., any hdd around 2A and other components need additional power from this rail. So it can't work.
Furthermore the motherboard just supports up to an athlon 64 x2 5600+
Even if the 370 would be recognized and would run (very doubtful), this graphics card would be bottlenecked and wouldn't run at its potential.
Look for a 750ti without extra power connections
Or look for a complete new system