at 4.25 grams, the 10K gold is worth about $67 in melt (today's value) You can calculate value based on % spread.
Personally, I simply google the melt value of "whatever carat" gold it is. There's several sites out there that will auto-calculate according to weight...
Most gold/silver shops will give you 75% without a batted eye. Find the right place and you can get 90%.
Best option is to sell it on craigslist or something (though that can take a while).
Before you sell, unless it's by weight, polish the ring. Gold and silver polish very well, and it'll remove any scratches in the surface. You can use a professional buffer, but there's no reason to. Personally, I use a drill with a rag wrapped on a drill bit, with a little car wax. I hold the ring in my left hand (with a glove on), and pull the drill button (it's setting on a bench) with my right. I just have a standard battery operated drill, nothing special, with a red shop rag. Turns old rings into new. Here's one I did last Thursday:
Out of the Ground:
Polished with Drill/Rag (you can see the red shop rag wrapped drill bit behind it)
Wiped down, and in the light.
This style ring (CTR) is $235 new from pretty much everywhere for the 14K. Melt value is somewhere around $30. Asking $80 on Craigslist. It's not worth selling for just $30, considering new silver ones are $49-$69. Someone will pick it up!
With the polish it's darn near back to new condition.
Probably the same for your diamond ring with a little attention. Shouldn't have any problem getting $100-150 out of it.
Skippy