What would you do?

Take it to a Genius Bar and get a quote on a repair.

 

Settings -> General -> Accessibility -> Assistive Touch

 

If you want more money for it sell it yourself on eBay or Craigslist. More hassle but you will get closer to fair value for it. Otherwise do what the previous poster recommended and wait for your 5S

 

Take it to a local reputable iPhone repair shop. Repair should cost around $70 for a genuine Apple part. Once repaired, you should be able to fetch the normal Gazelle rate, which is about $200+, depending on the condition. Had my sleep/wake button repaired on my 16GB 4s, and just sold it two days ago for $220 on craigslist.

oh btw, instead on Gazelle, try a Texas-based electronics buyer called Technollo.com. Before I sold it locally, I received a quote of $200 from technollo, where Gazelle only offered $190. Technollo also does not require you send the box or charger/USB cable, just the phone itself. This is awesome because you get to keep it handy if you have any 30-pin iOS devices still laying around.

 

My buddy had the exact same issue with the power button on his 16 GB 4S and got through it with the assist feature till the 5s came out. He might have been lucky but Verizon gave him $200 as a trade in towards the new phone and he put it towards a higher memory 5S. He said the guy didn't care that his phone had some scratches from normal wear or the power button.

 

I've never tried or heard of Technollo but I would recommend BuyBackWorld instead to sell your old phone. I know BuyBackWorld pays higher prices and actually delivers on their quote. I've used BuyBackWorld to sell over a dozen devices. Gazelle has a good service, but BuyBackWorld pays more and seemed to pay faster (I used Gazelle in the past).