My MacBook pro is up to date - no updates needed. I had tried restarting many times before posting here and before finding the answer to this question. I also tried resetting SMC and PRAM, checking the disk for errors using Disk Utility, logging in as a different user, and starting in Safe Boot to see if there was any change. None of those experiments worked.
Here is what caused the issue with the keyboard: Dropbox (the cloud storage service) has some issues where, using their default configuration settings, the documents you have stored in the cloud will show up in the Storage section of About This Mac as if they are stored locally on your Macintosh HD. In my case, even though I have over 100GB available, the way Dropbox was configured made the drive behave as if it was full - stating that I had 3.2TB of data stored on my 256GB SSD (which is obviously not possible).
Moments after resolving the Dropbox issue my A1243 Keyboard and Pro Mouse both worked perfectly again. Per Dropbox customer support (and confirmed by my experience), the fix is as follows:
"You may see some online-only files that appear to be taking up physical
space on your local disk, as macOS calculates the size of a file based
on logical size rather than physical size. You can however adjust your
Dropbox settings so that online-only files have both logical and
physical size set to zero. To do so:
1. Sign in to dropbox.com
2. Click your profile picture (or grey circle) in the upper right corner.
3. Click Settings.
4. Set the “Smart Sync update for Mac” setting to "On".
The
setting takes a little time to update in the backend so please wait
about 5 minutes, then restart your Dropbox app as follows:
1. Click the Dropbox menu in the system tray or menu bar of your computer.
2. Click your profile picture or initials.
3. Click Quit Dropbox.
4. Start Dropbox app from the Applications folder.
The Desktop app will then resync your files with the logical size set to
zero bytes. This may take some time to complete depending on how many
files you have in your Dropbox."
I hope this can help others experiencing this issue with Dropbox Smart Sync on their MacBook Pro disabling their USB keyboard and mouse. It's an incredibly annoying issue!