What to do when ebay seller won't respond?  

Paypal refund is your only option.
If you've paid, she's obviously obligated to refund your money, but you've little recourse-- except a sharply-worded negative-- if she doesn't want to honor the sale.

I feel your pain Brent, been...
I feel your pain Brent, been there and done that. I am afraid you have probably played all of your cards now and will end up with a refund. The old eBay saying of binding contract is rubbish on there, if the buyer/sell won't play ball there isn't much that can be done. If the tight gits won't pay extra for a reserve then they should honour the deal.

Yup
neither you or eBay can make them sell it to you.
The best you can hope for is a refund via Paypal and to leave a neg to warn others about the possibility of their bid not being honoured
You can also (in the UK at least) leave a 'non-performing seller' strike- a few of these and they're out.

Act quickly
You're not going to get the chair, Brent.
How long ago did the auction end? Ebay and Paypal have relatively-short time limits for leaving negative feedback and escalating a dispute to a claim; don't delay.

True. You have to act...
True. You have to act quickly. Few months ago, I won a beautiful mid century Lotte lamp for $10 and never received it ($25 shipping cost). I fill up a claim and I got refund. Make sure to keep all of you correspondance with the seller. Good luck.

Thanks, everyone.
I escalated the paypal claim today. At least I get the refund.

Maybe.
Maybe you get the refund, maybe you don't; if Paypal decides a claim in your favor, but there's no money in the other party's account, they may tell you that they CAN'T give you a refund... But that they'll make some unspecified effort to get some money from the other party at some unspecified time in the future, blah blah blah...
When I get that form-letter from Paypal, I just forward it to my credit-card company and initiate a chargeback. Never had a problem getting the money back that way.

Your eBay item has been shipped
That's the email received today, anyhow. I will have to believe it when I see it.

UPS
So, I actually received a UPS tracking #, and today the package shipped. Part of me is still expecting to open the box and find a different chair, or maybe a box of rocks, but so far so better than I expected.

Blah Blah Blah or How I Managed to Misunderstand You
Haha. Can't wait to see the outcome!
But, you have to admit. It sucks for the seller. Having made so little and having to go to the effort to pack and ship.
Admittedly, their fault. But, sheesh. My guess is that they never planned to stiff you, but it's easy to drag your feet on something that has no real benefit to you.
Morally it makes sense to get off your arse and make good on your word. But who is even moral anymore?
I wouldn't do it. But lots of good people, even some of my friends, would be just as likely to waste time on a bothersome task. I hope you get your chair. How will you recover it?

Hopsack
I intend to recover it in charcoal hopsack, probably through retroredo.com. I have a red sofa, so black and gray help absorb the color.
Your evaluation makes sense. I'll let you know if I do actually get the chair.

I was watching this auction
And the legs look weird. I think they are probably just installed wrong. Good luck!

Those legs bothered me, too.
They're all akimbo.