I have always built my own systems and for friends/family, only a couple of times it worked out cheaper to buy pre-built as all they wanted was basic for internet and office. I still maintain and upgrade my own and friends/family systems so unless there is a major problem it's cheaper just to replace the faulty component.
The Radeon HD6850 works fine with Windows 7, although there had been some issues with freezing and BSOD with certain manufactuers. One thing I never do is load the drivers that come with the cards, they are only tweaked versions of the chipset manufactuer so I always use it direct from them, I use Nvidia card in my system so get the drivers off there site but in your case the driver download would be from AMD but then I do that with any card.
As you said the engineers said the motherboard was knackered and the voltages it could be that causing the other problems, if the voltages are spiking it can damage other components or especially with a graphics card under voltage and the card won't run correctly. Probably find if they said they suspect the motherboard was knackered from new then that is why you had so many problems with the system and having so much replaced.
If it was just the motherboard I would have said just replace that but you mentioned getting new graphics card, CPU and hard drives, although if possible I would try the CPU, graphics card and drives on another system if you could rather than paying out good money if it's just the motherboard that is knackered. You can get budget boards but then I would pay a little extra and go for mid range if you did that as you pay for what you get. So if you know anyone that has a system they are willing to let you test the drives and graphics card on then I would test them first, if they are newish drives they should have SMART on them or download the drive diagnostics from the manufactuer site and run the self tests to tell you the state of the drives, the graphics card is easy as if that works just use a site where you can stress test it plus you.
To give you an idea I just upgraded a friends system few months back with an Asus P8Z68-V Gen 3 motherboard, 8GB of 1600Mhz gaming ram, i5 2500K CPU and a 500GB Western Digital Cavier Blue 6GB/s Sata drive and that cost just under £400 with the motherboard and CPU being the most expensive items. So based on that if you were using the system for just basic things then you could probably build around what you got for around £325 with an entry level i7, be cheaper to go for an i5 2500K as that is faster than some of the entry level i7's, semi budget motherboard, budget graphics something that is still fast like a Nvidia GTX 500 series as they dropped in price since the release of the 600 series, same as AMD if you prefer them and my personal choice a Western Digital drive.
I always used to use either Seagate (they own Maxtor now so buy a Maxtor external and you will find a Seagate inside) or Western Digital but I found that the Western Digital Cavier range to be very reliable and slightly faster, especially over 500GB as my own system I got two 6GB/s Western Digitals and a Seagate Barracuda and that is the slowest of them all despite on paper it should be faster. So now I tend to fit Western Digital rather that Seagate, although again all depends what you want.
I'm lucky enough to have a local shop that more or less matches internet prices, although I do buy a lot of stuff through him so much easier than on-line of there is a problem as you got all the hassle of returns but like someone said you can pick up secondhand stuff off eBay, although it you wanted to go new there are places on-line like:
Overclockers UKEbuyerMicro DirectDabsAria TechnologyNovaTechScan Computers All of these sell the replacement parts or pre-built budget systems. If you choose to go along the pre-built route then often like I did with a friend worth paying that little bit extra for a system that has the expansion slots as some very low priced systems have very little upgradable options, most come with onboard graphics and sound but I prefer to disable these and use a dedicated card for that and that onboard feature is just a backup if a component fails until you get a replacement.
Personally though before deciding I would see if you know anyone willing, even if they have an old system they don't use to test the graphics card and drives as seems pointless paying out for things you don't need to replace. Be nice if someone had a motherboard laying about to test the CPU but then that should hopefully be OK as the new ones are designed to prevent damage, although saying that all that side of things is run from the motherboard. Other thing that may have fried your motherboard is the power supply, that's something else I always use a decent one of I'm currently using a OCZ Technology one but the Targus, Antec and Cooler Master are decent ones, there are some other makes so good idea to check out what the popular ones are.
Hope you get it sorted anyway.