Changing the water was probably a good thing to do if it didn't look clear.
Try checking the pH levels in the water. Make sure it's pretty neutral.
ANother thing to check is the water temperature. Betta's don't like cold water at all... When I got Leliia (as she was sent to me via USPS mail, as lame as that is :D' ), she was freezing cold and hardly swam... in fact she was on her side. D: But after I let her sit in warm water (while she was in her cold bag of water, of course), she perked right up.
Actually, rereading over what you said, it reminds me of the pretty crowntail my sister Meggy has. He also wasn't eating, moving much, etc. His water was fine, clean... and Meggy did water changes anyway to make sure. It ended up that he had a fungal disease! Now he's completely covered in the fungus and barely alive... I gave her a few fast tips for helping him out, but we'll see if he's still alive in the morning.
The best thing to do for your betta is get Betta Revive. It's a tad expensive for .8 fl oz of medicine, but it really does wonders. I recommend you get this stuff and follow the directions on the back as soon as possible, if your betta does have a fungus disease.
Might I add:
Fungus diseases (as I read) are caused by the fish's stress coat disappearing or being at a low level. (I promise I speak english better than this, but it's 1 am for me. xD; ) Without the coat, it makes it easier for the fungus to attach and eat away at your fish.
Also, if you're not sure what to look for at the pet store, here's an eBay link for it that fully describes the medicine I recommend: http://cgi.ebay.com/Aquarium-Solutions-Betta-Revive-0-08-Oz-Item-71100-/360061614111?pt=LH_DefaultDomain_0&hash=item53d558 381f
I really hope I helped. My sister's betta Valentino was gorgeous (as all Siamese fighting fish typically are), but it may have been too late for him. I'd love to know that I helped save a betta.