Your PSU is likely a low quality unit if it has no PCIe power connectors. The one for the motherboard is CPU power and a different configuration than PCIe power.
You definitely need a new PSU and should get a good quality one. Here are some choices for a range of budgets. I don't know what GPU or CPU you have. So to play it safe I'd recommend at least 600w.
Good quality
- Corsair CX or CXM (black letters not units were CX/CXM are written in green, those are older low quality units)
- Seasonic M12 II Evo (should be Evo not older non-evo model)
Very High quality
- Corsair TXM (Black no Yellow letters)
Top quality all nearly equal
- Seasonic Focus or Focus Gold
- Corsair RMx/RMi
- EVGA G2/G3