I'd estimate that to be about 380 floppy disks. Great find.
Any driver disks are definitely a plus. There's definitely some old hardware floating around that is unusable because the drivers are missing, like the Megascreen 3 video card in my Macintosh SE.
Have you replaced the capacitors on the logic board yet? If they have not been replaced yet, this is the first place to start troubleshooting. Even if the original capacitors don't look bad (at least without heavy magnification), they are almost guaranteed to be bad. They are likely one of the reasons this board is not working.
I think the Analog Boards on the Classic line are supposed to be temperamental, and it sounds like you may also have a power supply problem too. If there is not enough voltage going into the motherboard, there will be a checkerboard too.
This board definitely looks like it is in good shape, and I think it will clean up quite well!