you've made my day, someone who read the post and understood that this was a laptop! -my hero.
you'll need something like this
which will let you add the drive as a drive in a regular PC.
or something like this
that will let you put the disk from the broken laptop into an external enclosure and have it as an external USB drive.
the one I linked is one like I have that supports both IDE and SATA laptop disks, but you might want to buy one that's just specific to the drive type that you have.
as for password protection.
the password that you log in as usually just locks windows, and does not affect files.
however, if you had the option "make my files private" turned on then the files will not be accessible easily from another PC.
your other option of course is that you could see if a friend has the same laptop and see if you can have them charge the battery for you so that you can move the files.
also if it's just the power plug that's broken you may be able to take the machine apart and fix this yourself. -or a friend with good soldering skills might be able to fix this.
almost off topic, I don't know where you live. but when my phone broke (the power connector came loose on the inside), I took it to a shop in london where they did a remarkably good job of fixing it as they have the tools (good microsoldering station for suface mount components), expertise, experiance and skill.
it also wasn't too expensive and the staff are quite friendly and reliable.
they specialise in phone repair, but if you are in the UK you could give them a call and see if they'd be able to have a look for you, (they are based in Wimbledon, London, UK and their website address is http://www.turnonyourmobile.com/
) they do offer a postal service, but if you fancy a day out the shop is reasonably easy to get to as well being just a short walk from the train station at wimbledon (which is accessible from both national services from the south and the underground).
I don't know what the price you've been quoted is, but the price to fix my phone was something like £40 - £50