After 6 months, a problem with a machine goes through warranty repair, not exchange at the store. This is standard operating procedure for just about every tech product, not just Macs. Call Apple support, and have them walk you through a diagnosis. That's what the 1 year warranty is for.
I think any return/exchange with the store is out at this stage, sorry to say. Are you asking about a private dealer who might make a trade deal with you? If so, I think there are options there, but you will pay more for the transaction if you go through such a dealer, instead of doing it yourself, because you have to pay for their overhead. Plus, they are not going to touch it until it is in good working order, which means starting with Apple support for whatever might be wrong with it.
Check out any of these dealers for a trade-in.
From Mac of All Trades:
Below is the configuration you have submitted:
Model:Intel/2.16GHz iMac 24
Price: $740.00 (for selling it to them)
From a recent
ebay auction:
Apple iMac 24", 2.16GHz Core 2, 3GB RAM, Applecare '09
$1352
The difference being the cost of going through a dealer. I see brand new 2.8 Ghz Alum 24" iMacs for about $2049 and refurbs for $1899 at the Apple store. So depending on how you do it, you may lose somewhere from a few hundred dollars, to upwards of $1000 or more.
I hope some of these links will give you some ideas and resources for how to go do some of this type of research on your own. Good luck!