i would recommend to go with 4 GB as recommended from Apple, I installed 8 GB and didn't noticed significant difference. Whether or not more RAM will benefit you depends completely on your usage. I have my Mac mini maxed out at 8 GB, and I wish I could stuff more in there--I get a lot of pageouts, depending on what applications I have open. In general, it behooves one to install as much RAM as one can afford. Especially if one uses Adobe or other memory-hungry apps.
Even assuming the LB is OK, that computer at this point in time is only worth $500-600, in my opinion. Probably not worth the effort, sadly. What other components are missing? PSs are only about $120 and HDs are cheap. Just wondering what it needs that's worth $600.
If you're running OSX, you can boot to the system CD and look in the Utilites (or possibly another) menu for the password reset utility. Resetting this password will let you log on and install software, but without your original password, your keychain's stored passwords will be inaccessible (for email, etc.) If you're running OS9 then it's the firmware password. Sorry, I can't remember if that can be bypassed or not. Here's another article that may be helpful: http://support.apple.com/kb/ht1352
Can you describe the "remote install OS X window"? While you're running in OS9, can you open the Control Panels/Startup Disk window and choose your OSX installation there? If the "remote install" window is actually the Netboot window, this should fix that.
An important thing to do with iMacs of this vintage is to open up the back (there are 3 screws along the bottom edge) and check the capacitors carefully for swelling or leakage. Shine a bright flashlight into the holes of the power supply; sometimes you can see if there's a bad cap in there, which could cause power issues. See how to take the back of at iMac G5 17" Model A1058 Power Supply Replacement
Can you try booting while holding down the Option key? Do you get a choice of OS9 or OSX? Failing that, try booting while holding down the X key. This is supposed to start up in OSX. Been so long, I don't remember if it works just with Boot Camp or also with OS9, but it's worth a try.
Assuming you've checked the partition map per David's suggestion... According to MacTracker, this iBook came with 10.3 installed, so it might not run 10.2. If you didn't make a a typo in your question, are you sure this installer is compatible with your computer? If the other iBook you used is a G3, then maybe the 10.2 installer is the one that came with *it*. Which also explains why the 10.2 installer would boot the other iBook.
If your computer supports 6gb, I believe more RAM would give you greater benefit than the nonexistant or negligible advantage of interleaving. Apple's RAM limits are always based on what chips were available at the time the computer was manufactured, and they never update them to reflect current availability. Mactracker is an excellent source of information, and it's free. Online, there is http://www.everymac.com, which is a little harder to navigate.
Grasping at straws here... You could try removing the battery, unplugging the power, and letting it sit for 24 hours and see if that brings it back to life. I assume you're not getting the startup chime? If you are, there are other steps we could offer. Have you considered it may not be getting enough power? Do you have access to another power adapter to try? Try it without the battery installed.