Many games don't work with forced v-sync in the control panel because the forced options in control panel are usually(unless they finally changed it) only for opengl settings as officially trip buffer and vsync calls have to come from the game under some stupid stipulations from MS of the DX spec(again afaik).
Download Riva tuner, install, then from the folder or start menu look under Rivatuner and run D3Doverrider. IT will "try" to override the DX calls and add the triple buffer and v-sync calls which enables it on a LOT of games that drivers can't override directly(because they only get WHQL approval most likely if they strictly adhere to the DX spec, which most likely still stops them adding the option to force in DX, because MS are still rather retarded rather too often).
Thats one thing to at least try, another thing is odd syncing issues for desktop stuff, I'm not really sure why but a bunch of screens I've had often set themselves to 59hz rather than 60hz. It could be an issue like that, drivers/os updating at 59Hz, monitor reading at 60Hz, it will always be ever so marginally out. Try forcing 60hz in the control panel, try new drivers for the monitor, try DXupdate from microsofts site to make sure you're up to date, try new gfx drivers.
Personally I'm starting to get miffed that things that should have been standard, well a decade ago are still a little buggy in these situations.
Powerplay, for both Nvidia and ATi afaik, can have issues as cards want to save power one way and OS wants to save power other ways, whack everything into full power mode in the OS power options and disable lower 2d clocks if possible in Nvidia control panel, been a long time since I used Nvidia drivers so not sure if the option is there.
For Ati, download GPU Clock Tool from a site called Techreport, you can also get gpu-z there which lets you monitor current speeds and temps and things. in gpu clock tool just set normal 3d clocks for your card, it should over ride powerplay drops in speed, it will only change it till you reboot so if it doesn't work one reboot, never use it again.
Few things to try there, after that I'm not sure what else you can try off the top of my head.
Personally I'd also ask overclockers for a 4870, or the price difference between the cards(if they changed cards and didn't offer the difference that is) because frankly you've paid for a system with one card and now have a slower 20% cheaper card in.
You could also ask them specifically to take the computer back, try some games on it and see if they can find settings to fix the tearing.
Sometimes tearing is appauling, other games its less of an issue, some screens do seem worse for it maybe due to the way they process the data or call for the data. But I'd think something I've suggested so far should/could work.
Though its ridiculous, theres still one/two games I just can't get to work with v-sync no matter what I've tried.
So far, Lotro + windowed mode I can't get vsync to work, or if it is working its not remotely effective, but its also not "that" bad.