You're not providing enough information.
The Radeon HD 7850 needs two 6-pin PCI-E connectors for power-- does your PSU have these? In addition, the minimum recommended wattage/amperage is 500W/20A. Does your PSU meet this?
You said Core 2 Duo, so your motherboard is a Socket 775 board. What processor do you have installed? There might be a bottleneck.
The Radeon HD 7850 needs a PCI-E x16 interface. It's safe to say that your motherboard probably has one of these, but it can't hurt to check.
It'd be a great help if you'd post your exact motherboard model.