As others have pointed out, Croc Skinks are very, very shy - and yours may not be sick, just shy. Having said that...
"The only lighting this lizard has was a heat lamp. Some info says you must have a uv light and some say you don't."
Right. Lighting seems to be necessary when young, not so necessary when older (though a D3 supplement should be used if you don't have the light).
"Then some say there is two different types of lights etc."
UVA and UVB. You want a light that provides both. I leave my light on 6 hours a day and have no problems (I don't use a D3 supplement, either).
"My problem is i think the lizard is weak/sick. It does not respond to anything except when you pick it up and when you do that it only opens it eyes and then it falls right back asleep."
Sounds familiar.
I have a male and two females. The male gets AGGRESSIVE, and even bit me once (for all the good that did him - their bite just isn't that strong). The females generally freeze up, then go into their defensive roll/thrash, then freeze again when handled. Hold them too long, and they'll tend to go to the bathroom on you. 
Here's a checklist you can go down that might help you determine if you're pet is sick:
1) Is there stool? If there is white fecal matter in the cage (or brown "cocoons" in the water dish), that's a good sign (though you should clean it up).
2) What is the temperature? I know some people keep their entire cage/terrarium at 80 degrees, but that's a bit too high. During the day, mine goes left to right 68-80. In the evening, I'd say it is closer to 65-75 (the majority being around 70 the entire time).
3) Are you using a vitamin supplement? You should be dusting the food with a vitamin supplement - sometimes calcium, usually something with a bit more variety. I will tend to dust my crickets until they look like little ghost-insects that stand out against the bark/soil of the terrarium. These crickets then go into a small ceramic sauce dish I bought at Meijers for 99 cents (most of the crickets can not get out of it but the skinks easily get in).
4) Is there water? By water, I mean a big enough water source that the skink can submerge in it. I went out and purchased a "pool" with little stairs on it, but I also have ceramic "pet water" dishes that they jump into and curl up in. Having these water dishes is more important than keeping your humidity high.
5) What is the humidity? Humidity is not as important as one might think if there's a pool of water. If you can get it to 85, that's great! If you can only get it to 60, I wouldn't worry too much - just make sure to use a vitamin/shed spray on them every two weeks.
6) Are there multiple food sources? Don't just give them one type of food, give them a variety. My primary food source are 3/5 week old crickets (purchased under contract and occasionally by PetsMart). As well, I put earthworms (red wigglers) into the terrarium that they can dig up when they feel like it. In between cricket feedings I fill a bowl with 30% honey / 70% water and leave it in their - they seem to like that a lot. Finely chopped fruits are also placed inside on occasion.
Worst case scenario - take your pet to the vet. It may have parasites or an infection, especially if it is wild-caught. 
Good luck with your new skink!