what are you feeding him? how are they gutloaded and what is your supplement schedule and what brands? What is the humidity? How do you offer him water (mister, dripper, humidifier, etc.)? Does it cool off sufficiently at night (10-20 degree drop). What light schedule do you have him on? How are his colors?
It is Friday, so have a vet lined up just in case. We can't diagnose just help the best we can. Not opening his eyes is obviously not a good thing. Can you hear him wheezing when he breathes or see anything that might indicate a URI (upper respiratory tract infection)? Do you see any crust around his eyes? Does he EVER open them? Have you had a fecal done to rule out parasites? The more info you can give us the better our collective knowledge can help troubleshoot.
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Chameleon Help & Resource Info
1.0 Nosy Be Panther Chameleon - Cyrus
0.1 Veiled Chameleon - Luna. She's now hanging from her big jungle gym in the sky
1.0 Beardie - Darwin
1.1 Side-blotched lizards - swifty and blotcha for now 
0.2 felines - Kyndra and Lita
0.1 African Clawed Frog - Skipper
0.1 Chilean Rose Hair Tarantula - Rosa Leigh Died 4/21/06 
0.1 Goliath Bird-Eater Tarantula - Natasha donated to science 4/4/06
?.? Pinktoe Tarantula - no name yet