Is changing the battery in this notebook as simple as merely sliding in the replacement battery?r

SOURCE: Asus a6000 keyboard

Keyboards are most generally held by screws in one of two places. 1- On the bottom, could be marked with a K, With bottom screws, the keyboard may have tabs on it holding it, you will need to pry the tabs gently out away from the plastics. 2- towards the top of the keyboard under the power button strip. Try this link, you may be able to find a breakdown diagram for your machine there.
http://repair4laptop.org/notebook.html

Don't be afraid to remove all the screws on the bottom of the machine if you're unsure as to which are for the keyboard, it won't hurt anything as long as you get them all back in. If they're marked with a B, it's a motherboard screw, and P is for plastic casing.

SOURCE: asus A6R -No power at all

yes repairing laptops is tricky, not like a desktop pc, so that sounds about right, and yes the port on the back where the power plugs in will wear out and break. thus not charging your battery no matter what power adaptor you use. so yes ask them if they offer a no fix no fee policy on that repair. and when they do fix it. check what warrenty the repair comes with. other than that it sounds fine to me.

SOURCE: computer beeping and saying reboot and select proper boot device

When you reboot, go to BIOS, restore factory BIOS settings. If that doesn't help, you'll need to reinstall your OS.

SOURCE: How can i reboot my laptop?

It is either not seeing the HDD and/or the boot sector on the hdd has been damaged. Any repair you do will only be possible after you boot to an environment. If you can get a bootable CD made, that would be one option. Bootable USB is another. Once booted, you will then be able to examine the HDD to see what the problem is.
Does the bios show a HDD at all?

SOURCE: New battery calibration, drain battery, windows will not boot

sounds like OS was not fully installed properly----Reinstall.