If you transplanted the innards from an HP prebuilt, what was the SKU/model for the prebuilt? To answer the question in your thread title, even if the unit was reliably built it couldn't power the entire system. So, no 300W will not cut it. You're going to need more like a 5000W or a 550W reliably built PSU.
Does the psu come with the needed 6 pin pcie connector?
Can you tell us how many Amps on the+12V rail?
Sure it has only one +12V rail? Because that is low, equals to 180watts.And the the amps of 12+ is 15a.