So recently I've started selling a load of stuff on ebay, been buying stuff for years of course.
DOA Items.
If the item is marked as used the seller is taking the risk of DOA items, your entitled to a full refund even if marked as no returns but remember old hardware is going to fail eventually.
Take the approach it died in transit and not the seller is trying to rip you off.
Contact the seller first letting them know what troubleshooting steps you have tired.
This shows the seller your not an amateur that doesn't know how to use the part and they may have a suggestion that you didn't think of.
If your polite, something along the lines of I'm really sorry but I received xxx but it doesn't seem to work. I've tried .....
I've never had any trouble with refunds.
Not sure in other countries but in the UK the rules state seller needs to refund both the item and shipping costs (including returns)
I only found that out few months ago when I sold my first DOA item, not sure how long that has been the case. Dude got a bit upset when I said I would refund the cost of the item and left off shipping and pointed this out to me, but once I double checked and said yes he's right, I'm wrong and new to this he was very friendly even offering tips, etc now he knew I wasn't trying to rip him off.
Items in the spares/repair category are often simply untested. I put this in the heading but now the risk is on the buyer, items will always sell for less but it's a risk as no returns does mean no returns.
Partial refunds
I've only experienced as a buyer. I'll contact the Seller saying item works but xyz is wrong how do you want to proceed? The seller may give you a better deal then you were expecting. If its a worse deal then counter offer with your own or return it.
Missing Items
This is actually where I've had the most trouble both as seller and buyer.
As a buyer typically I contact the user 2-3 weeks after the items ETA. typically they refund no questions but it's been small value items.
Once I had to open a case from a part arriving from Canada as ebay's 30 day window was about to close. I had already messaged the seller so told him this is what I was doing and sure enough the package arrived within the week.
As a seller I've had 2 items go missing. I'm using eBay's tracked service from Evri so can quite clearly see the item hasn't arrived. Both times the buyer has contacted me first.
I'll reply letting them know I can confirm it's not arrived and going to open a case, pass on any updates I receive, then ultimately just have to refund the buyer, with Evri giving me at least a partial refund.