I buy laptops for work stuff, because I have to be compatible with the Microsoft universe, and have plausible deniability security wise (i.e., I exercised due diligence in a way your IT guy will understand and accept as valid).
For everything else, computing hardware and software is free. I kid you not.
First, ask a favour and find an external monitor to plug into. The guts of your laptop may be just fine, even though the display has gone kaput. All your data, passwords, etc. are almost surely intact on the internal hard drive. Any external LCD monitor under 20" is basically free for the taking. You could operate with that for a long, long time.
Second, the hard drive from you old laptop can be plugged into another compatible machine, and you can retrieve all your stuff.
Third, for the truly hardcore, there are free laptops out there everywhere. Just ask around and you will be surprised. Perfectly good hardware and hard drives, but the operating system is some older version of Windows that nobody wants. Wipe the drive with DBAN (Darik's Boot and Nuke), which completely overwrites all the old stuff multiple times. Install a good Linux flavour like Linux Mint (my favourite), which is so close to Windows it's perfectly intuitive, and you are fully operational for free.
Fourth, though Authority doesn't care for it, you can scrounge perfectly good components from recycling bins. Waste is evil, IMO. But you will need to be very discreet, and have a little tech savvy. And wipe that hard drive with DBAN. Do you really want to know what's on there? Yikes.