Most laptops work fine without their batteries. Some don't, it depends on how they're wired back there. However, this should not affect anything else in any way. If you manage to turn it on without the battery, it shouldn't affect the hard drive at all.
If you want to check the hard disk, flip it upside down and look for a slot fastened with a few screws. There should be about 2-3 of them, one for the hard disk, one for the RAM chips, and maybe one more for some other skulls. I can't tell you which one is gonna be the right one, so you just gotta go for trial and error to find out. When you find the drive, you should be able to tell if the cords are plugged in correctly. If a hard drive isn't present at all, fear not, because they're real cheap these days. You should be able to find a retail 40 GB 2.5" hard disk for like 30 bucks, or 120 for $50.
-edit-
I didn't see the part about you opening it and checking it at first. If that's the case, it might be the hard drive itself that's broken. If you know anyone with a laptop, you can ask them if they'll let you test your hard disk in their laptop, just to see if it works for them. If it doesn't, it's likely that the hard disk is faulty and you'll need a new one. If it does work, it's likely to be a more serious problem, and I can't really help you. Testing your hard disk in a different laptop will not ruin any of the data stored on the laptop that was originally in the other laptop.