I'm in Chandler, AZ and have a 1 and a 1a, but before you think of driving anywhere, I'd suggest doing what the Osborne 1 Field Service Manual states for a keyboard problem.
1 - check for a stuck alphnumeric key
2 - replace the keyboard cable (thought I had a spare but can't find it right now - may be able to make one though)
If the problem continues, they say to replace the keyboard (I have no spares), and if the problem still continues, replace the main logic board (I have a couple spares).
I'd also check the voltages from the PSU.
You should also check the RAM (which is tough to do when you can't get the disk drive to work because of the keyboard problem).
A year ago, I bought five of the full travel membranes for Osborne keyboards that someone had sitting in a warehouse for years.
I got them cheap and it's a good thing I did - only one of them worked, and that was all I needed.
The rest went into the trash about six months ago.
I had an Osborne 1 do some weird stuff once before, and it was due to a bad RAM chip.
Also try lifting up and/or pressing down on the keyboard connector where it connects to the actual Osborne - I had one that didn't work because of a bad connector, and when I lifted up on the connector everything worked as it should.
I assume your sign on message isn't flashing (if it is, the keyboard probably IS toast).
If you felt like making the drive to test the keyboard, we could do that, and also check the RAM, and test the disk drive alignment while we were at it (you'd just have to bring a dozen Bass ale with you).
PM me if you want to try a spare cable, or make the drive.