As Hugh said, dry batteries are a bad sign. But, to determine how bad, you've got to fill them with distilled water, charge them then test them. Once fully charged, you should test each cell with a hydrometer (which you can purchase from an auto parts store). You should also have a digital volt meter handy. Jot down all of the hydrometer readings (of specific gravity)from each cell. You'll need to research how close all those readings should be to each other in each battery. I suggest going to the battery manufacturers page for this info but the hydrometer instructions may tell you this.
Safety moment: Battery acid is corrosive. There is a possibility of splashing it as you do this testing. You should buy and wear safety goggles as you do any work on your batteries. Also, remove metal jewelry so that you do not allow it to come in contact with any of the battery terminals (very harmful for the jewelry and your fingers). Finally, I keep a garden hose nearby in case I get splashed with acid. And, wear clothes you don't care about because you will get some acid on them and it'll cause small pin holes (think what it does to your skin, too).
You will most likely need to look into your charging system and see if it is operating properly. Many of our rigs have a Xantrex Inverter with built-in battery charger but the Xantrex control panel (ours is in the kitchen above the dining area) allows various parameters to be setup. You should check how the previous owner may have setup yours. Depending on the results of your hydrometer check, you may end up deciding to "equalize" your batteries. This is also accomplished from the Xantrex panel.
If you do decide to get new batteries, take a look at the websites for some of the bigger manufacturers to see what size batteries will fit in your battery box. As I recall, Interstate had batteries of 3 different ratings that were identical in size (but in weight). I believe I choose the U2400. Here, you might have to decide how much of what kind of camping you like to do. We like to boondock and only have the tiny solar charger panel so I opted for the larger capacity batteries. If you typically like to have hookups, you might opt for the lower capacity batteries. Also, I've got 6 House Batteries while you may have 4, 6 or 8. Don't forget to take a look at the Sams Club Golf Cart batteries. And, depending on a lot of factors, you might be money ahead by paying a much higher cost up front and getting the newer style gel batteries instead of the lead acid batteries I'm assuming you now have. (If you're not into all the maintenance that goes along with lead acid batteries, maybe you shouldn't get them). If you do go with 'gel', you need to reset the Xantrex panel so it knows what type of battery it is charging.
Buying tip: You should take a digital photo of your battery posts with you if you go to buy batteries (to take home to install). My old batteries had a horizontal hole thru the battery stud so you'd insert a horizontal bolt to hold them in place. I ordered the batteries over the phone, and forgot to mention this small fact, and received 6 batteries with vertical studs. All I had to do was roll the battery cables on their sides but that did end up involving a lot of bending and one particular cable that was just barely long enough.
You probably want to arm yourself with some information. As Hugh said, you ought to do a Find in the Alpine Forum. Here are a couple of other sources of battery information:
(My personal favorite)
If you do install new batteries, how are you charging them? Are you using the charger built into the Xantrex inverter? Are you able to hookup to shore power while your rig is stored between trips, do you turn off all your battery switches and have you checked for small "parasitic loads" to insure that your batteries aren't being constantly drained without you knowing?
My choice was to leave the stored rig connected to shore power, install two very small (about 1.5 amp) "smart chargers" (one for the Chassis batteries and one for the House Batteries, my favorite brand here is Battery Tender); and turn off both the battery main switches. During storage, I do not use the Xantrex charger.
Finally, some of our rigs have a system which automatically (or manually by pushing a button) sends water from a reservoir to the battery cells thru clear tubing. Some people report that their system doesn't work and they don't like it. Our system works fine and I do like it. But, there was at least one report of the wrong size part (in the watering system) installed by WRV for the particular battery that a customer had down the road. So, if you've got one of these systems, do not assume that what you have is right for your current batteries or for whatever you choose to replace them with.
So, you don't have a simple problem and there isn't really a simple answer.
Best of luck!