I think you have apoor power supply. Certified are recommended.
ATI Radeon HD 4870 System Requirements
500 Watt or greater power supply with two 75W 6-pin PCI Express® power connectors recommended (600 Watt and four 6-pin connectors for ATI CrossFireX™ technology in dual mode)
Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU
for a list of Certified products. http://ati.amd.com/products/radeonhd4800/requirements.html