You might actually be OK with 250W. I've got an old system that I upgraded to a 250W PSU with slightly lower ratings than yours, and it has an ATI Radeon 9700 pro, which uses the same amount of power as the GeForce 6800.
Provided the amount of other components in the computer are similar it should work fine. My computer has 2 sticks of ram, 1 HDD, 1 DVD drive and an Athlon XP3200 processor. It also has more powerful fans fitted than stock, because the case is really cramped and the airflow is bad without them.