I have a 250W power supply but it asks for a 400W power supply and I want to know if I use an adapter on the two 4-pin connectors I have to get a PCI-E connector will the graphics card run? The card I would like to get is an AMD Radeon 6850.
I would not do it. There are adapters, but the power supply will die trying to run the system.
The card it self will use about 100watts(from the 12 volt rail) most of the times(peak being about 130watts).
So even if the entire power supply is dedicated to the 12 volt rail(and its not, but there should be a rating on the sticker), that does not leave a lot for other things.
If you take the amps on the 12 volt rail x 12, you get the wattage, but for a 250 watt unit i would guess about(14-16 watts in most cases)
It just not enough power to be reliable. When you get a new power supply(assume you want to run that card). Look at the 12 volt current. Some units have more then one 12 volt rail, in that case look for a combined power.
It may or maynot work. But the real Answer is No, because if you do get it to work, it will work at a very slow speed and will run choppy and may crash often. And worst yet you may end up damageing your card, so i don't recommend doing it.
Don't forget to get quality brand PSU, like Antec, Corsair, Seasonic. If you get some cheap PSU, even if it's labeled 700W, due to cheap power supplies using cheap materials, it might not work. Also cheap power supplies tend to kill other parts of your computer, so don't cheap out on PSU! Corsair or Antec 500W will be more than enough for your needs.
Every so often 'egg has the Rosewill Green 630W for sale for $50 even, and if you get the newsletter they often do another 10-15% off + free shipping on power supplies. When you can catch it at that price, its the best sub-$50 power supply I know of.
Its the cheapest, rock solid power supply I know of. They have maybe 1% more DOA than the top brands, but you'll get stable power from it, and they are built properly internally to ensure you get good filtering, virtually no ripple, and all of the watts you pay for (and more).
You wont need 630W of power to run your system, and a 6850, but its always nice to have room to expand a bit more, and not have to worry if throwing in 3 more drives, or whatever else is going to put you over-budget on amps.