I've posted a couple times here trying to figure out what I want. I went to a local pawn shop and they had a Thompson Center Renegade cap lock for $150. Decent price, what to look out for, any known problems with this model, best way to check for rust all the way to the end?

Good guns, you can convert it to flint ignition fairly easily, and stepping up to .54 caliber is possible as well.

Buying one used, at minimum I would take a look down the bore with a flashlight or bore light.  You'll want to see bright shiny metal with no dark spots.  Running an oiled patch down should produce only a little bit of gray carbon and maybe a faint touch of light red from rust would be acceptable.  Any black from being shot and put away without cleaning, or lots of rust red, and I'd buy it with the knowledge that you're going to be replacing the barrel.  There are a few places where drop-in replacements are available, Green Mountain barrels come to mind.

I would only pay $75.00 at the most for it. Pawn shop more than likely paid about $50.00 for it. The reason for that is all the young bucks want an inline now so cap and flint lock are going for cheap. Like the man said check the barrel for 2 reasons one is like he said it maybe all rusted out and such, but the big reason is it may still be loaded. Make the pawn shop snap a cap on it first and see if it has some flash comming out the barrel.

Don't try shooting it to see if it's loaded. If it is loaded and the ball isn't seated it will bulge the barrel. It also could be double charged and do the same thing. Powder will stay good for a very long time.
Just take the ramrod and lay it against the outside of the barrel. Place the end at the breech and see where the rod extends past the muzzle. Then put it in the barrel and see if it is the same length. If it sticks out further it is loaded. You can also place the buttstock on the ground and drop the ramrod in the bore. It will bounce if it's unloaded and it hits the breech face. If it's loaded it won't bounce off the roundball.
If it is loaded remove the nipple and use a CO2 discharger to unload it.

Run a damp patch down the barrel, run a dry patch, then check the bore. Use a drop in bore light to check the bore.

Drop-In Bore Light

BTW, $150 is more than fair price for a Hawken Rifle made by T/C Arms Company. They make good weapons.

If the rifle is in good condition $150 is a fair price. I paid $220 for this LH .50 Renegade a few months ago:

Nice looking rifle Dave.  I concur on the conicals may shoot better in the 1-48

They generally do.  In my own experience, the 1:48 is a good compromise twist, it likes the lighter conicals and can be quite accurate with roundballs and light loads.  The rifling is a bit shallow and fast for heavy loads with roundballs, and some of the big conicals don't quite get stabilized like they would with a faster twist.  In my .50 I got key-holing with conicals over 400 grains, and roundballs would tear up the .015 patches (tightest I could fit with a .490 ball) if you shot over 50-60 grains of powder.  My .50 preferred Goex FFFg.

In the end, I was unsatisfied with the price of buying conicals and my ability to cast accurate ones myself, and unsatisfied with the "uumph" of light roundball loads, so I found a .54 caliber barrel rifled for roundballs.  That barrel loves to be stoked HOT, I shoot 110 grains of Goex FFFg with .530 round ball and .020 patch for my hunting load.  It requires a mallet to start the ball, but I put up softball sized groups at 100 yards, which is the best I can do with any gun and open sights.  That load will penetrate 36 inches of flesh and bone at 30 yards, chronographs at 1800 feet per second and beats .44 mag out of a pistol out to 110 yards, if the ballistics calculators are correct.