You are under several misconceptions about what you have. You have an iBook (per your thread title), not a MacBook. That means you have a PowerPC processor and not an Intel processor. There is a difference as Apple switched to Intel processors in 2006.
I am unable to make changes to the system preferences, install google chrome,
You cannot install Google Chrome. Google Chrome requires an Intel processor. You have an iBook that has a PowerPC processor.
or update plugins on mozilla firefox.
The last version of Firefox compatible with PowerPC Macs is Firefox 3.6. Even if you could update plugins it wouldn't get you very far with that old a version. If you want a more modern browser you can try TenFourFox.
I presume this is due to a lack in administrator privileges.
In the case of Chrome, it's because you have a PowerPC Mac and not an Intel Mac.
I would like to update this laptop as far as possible,
The farthest you can go is OS X 10.5.8 Leopard. Snow Leopard, Lion, Mountain Lion and Mavericks are Intel Mac only. Leopard retail disks can be found on the used market for about $100.
so I can stream videos and such.
Do not expect to do any kind of video streaming with a PowerPC Mac like you can with an Intel Mac or a PC. The youngest PowerPC Mac is eight years old.
My only guess to do this is to factory reset the laptop. Can you help me with this?
Buy a Leopard or Tiger retail disk, boot from it, wipe the drive and install the new OS.
I have tried restarting the laptop holding the apple + S keys, but it boots up normally without going to command prompt.
This is single user mode. And what do you mean by command prompt?
I am wondering what to do. I want to get this to work without getting a new OS X dvd. Thank you very much.
If you have an old OS X DVD, Leopard or older, but no older than Panther then that should work. Again, this Mac cannot run anything newer than 10.5.8 Leopard.
I'm going to guess here that you thought you were getting an Intel Mac (a modern Mac) and are expecting to be able to run current apps. You can't. This is a PowerPC Mac.
If that's a deal breaker for you because it's not what you thought it was then you might want to sell it.