Hi Bsheehan604,
I may be able to help. Lets take the easier topic first, the battery hookup.
This pic of yours, I cannot see close enough but this much I can state, Sunline use negative ground on the campers. And by your 2002 vintage camper, the heavy gage red wire would be pos (+) on the battery,
And the heavy white, would be neg (-) on the battery.
The pic is too fuzzy to see which polarity you have them on. Check and see.
Then we have 3 other wires to ring out. The 2nd heavy white wire appears to have a factory looking crimped on eyelet. Sunline in 2002 with slide campers may have done something different with the white 12 VDC ground wires. Have a look under the camper. One of those heavy white wires should go to a frame mounted terminal strip with with other white stranded wires going to it including a white wire fastened to the LP gas pipe as a ground. The other heavy white wire, "might" go all the way back to the wall switch that applies power to the slide motor. On the newer Sunlines, they only have one heavy white cable to the battery, but in your case, they may have run 2 heavy white cables and both are 12 VDC ground.
Check that and report back.
Next you have 2 small mystery wires.
A small faded red wire you now have on the same post as the large red wire is on. Not sure what that small faded red wire is. You are going to have to trace it back under the camper and see where it goes. Do not assume that is a 12 volt Pos + wire. It looks like a prior owner may have added something.
The next is the thicker black wire you have to the same terminal as the heavy white wire. That black wire may not be a 12 VDC neg (-) wire at all. Black is used by many RV accessories as a hot wire color. Trace that black wire and see where it goes. I cannot tell as your pic stops short, but if there is a power tongue jack on the camper, that black wire may go to it. And it is does, then that is the hot +12 volt DC wire for the jack. Most tongue jacks use frame ground as the negative DC wire.
Have a look at that and report back.
You have have a few different issues going on at the same time or they are interlinked too each other. First is to sort out the wires at batteries. If the little red wire or medium is black is still a mystery, let they stay unhooked and taped off for the moment. Take pics of where those wires go and post so we can help sort out what they may do.
If you have a charged battery, unplug the camper from shore power, (no 120 VAC power). With the battery hooked up to the correct polarity, the lights inside the camper, the water pump, the bath vent fan and other 12 VDC items in the camper should work off of 12 VDC battery power.
If they do not, which it sounded like they did not, then it may be your battery protection fuses/circuit breaker has issues. In 2002, Sunline installed a small Wooden junction box "inside" the camper to joins the 7 wire truck cable to the camper battery supply and to fuse both the slide motor drive power and the connection between the main 12 VDC fuse panel in the power converter and the battery.
This wood junction box is normally on the floor along the front wall of the camper. In your front bedroom floor plan, that might end up in the front cargo hole area or under the bed. Look under the camper for heavy 7 wire truck cable and see where it goes up through the floor. Then go inside the camper in that location and look for the junction box. It would have a lid on top with a few screws holding the lid on.
Inside that junction box there should be at "least" qty 2, 30 amp fuses. One 30 amp fuse (or a 30 amp self resetting circuit breaker) connects the heavy red wire from the battery to the main power convertor fuse panel.
The other 30 amp fuse, is on the truck charge wire line of the 7 wire cable. The 7 wire cable color would be black for that truck charge wire. See if either of those 2 fuses are blown. If the heavy red wire has a self resetting circuit breaker, then you would need to use a test light or volt meter to see if 12 volt power is coming across the breaker. You may have to hunt to find a frame ground white wire as they always did not bring up a white wire in that box on all floor plans. You might have one and you might not. Take a pic and post what is inside that box.
Since you have a slide system, Sunline often puts in a 20 or 30 amp fuse OR a self resetting circuit breaker to run the slide system. Check/test that 12 VDC power is passing through that fuse or breaker.
This wire testing assumes you are comfortable with working on 12 VDC systems like a car/truck. If you are not comfortable doing this, then stop and find a friend/dealer who is. We do not know you electrical background.
On your slide drive motor, you have the Lippert slide drive system. Your 2002 camper must be an right in the middle of when Sunline switched from Dewald to Lippert on the slide drives. I know many 2003 campers had the Lippert system, but the 2002 is sort of a gray area which have it and which don't.
This pic is of the Lippert (LCI) rack and pinion slide drive.
The slide motor may have been changed along the way. The early years LCI slide drives used a Venture manufacturing slide motor on the LCI rack and pinion slide system. Later, LCI started putting their own motor drive on or having it made for them with their name cast in it. You motor gear housing looks like the LCI gear box which did not exist yet in 2002.
That aside, there is a black and red wire coming out of the motor. By the pics, it looks like the black and red goes above the steel channel of the slide arm. And they join to a heavy black and maybe white wire or there color on the other side. Can't see in the pic. That motor is a 12 VDC reversing motor. The wall switch up in the camper switches the polarity to the motor to get the slide to extend out or retract back.
I tell you all this, as once we make sure your battery runs the lights in the camper, and maybe even the slide motor, then if the slide still does not run, we can start the next round of trouble shooting to see if power is reaching the slide motor. If your motor is wire nutted to the Sunline wires under the camper, with a helper at the slide switch, you can test to see if 12 VDC is going to the motor. Power only passed to the motor when the switch at the wall is held in. That tells a lot, one way or the other.
Hope this helps.
John