Agreed on the lack of tangible produce can make it feel like you don't accomplish anything. Oftentimes in IT roles, especially operational roles, your inputs only exist in temporary form, a request, a walk by, your 'work' is mostly identifying and researching 'what' to do (i.e. troubleshooting), actually doing it may have been very unchallenging and represent a small portion of the overall time, and the output may be unremarkable - restoring a system to its previous condition, for example.
Read the book Getting Things Done
What I've found a helpful adaption of those steps to an IT operation is put those inputs into a tangible form, a todo list, ticket list, etc. Make your finding out 'what' to do a tangible by product by documenting your work for yourself and others to refer to in the future. Call attention to the outputs by going over completed work to document lessons learned, provide detailed lists to your client/employer. At first it may sound like beauracracy you don't have time for, but long-term, the pure 'break-fix' cycle is unsustainable, it's not productive, people put in that position will burn out in weeks/months.

In communist China, search engine indexes YOU!

I explored offering this service as part of my consulting practice a few years back. Turned out hardware and software weren't the limitations, even if I could use a simple ADF scanner with a reasonably- priced temp staff. The limitation was the time to organize it into usable categories and make it the file name match the type of content, etc. I'm intrigued by some of the new software such as PaperPort http://www.scansoft.com/paperport/standard/ that apparently makes the documents searchable, minimizing the need to title and folder each scanned image, but I'm sure its relying on some kind of OCR and not sure how kind that would be to hand-written docs. As long as it allows a simple interface to tag each scanned image. You're gold.