This may or may not be of significance. I had a Browne & Sharp digital caliper years ago; one of the first out. It quit working at one point and when I pulled it apart, the glass Moire screen had come loose (probably due to to dropping). I aligned it and fixed it place and it worked. Now this was an optical scale with LED/photodiode sensor while your Starrett appears to be a capacitive scale but it is possible that a similar thing happened. There have been reports of capacitive scale DRO's not sensing or sensing erratically which have been attributed to pickup misalignment.
I would follow Dracen Knights advice and contact Starrett first. From other posts, it seems that they are very fair about repair costs for their products. If their estimate approaches a new replacement price, then pull it apart. At the very least you will learn something about the technology used; at best you'll have a functioning caliper.