Sorry, but unless you have some exclusions to your "30 day no risk money back gaurantee", you are stuck. By stating that it is 'no risk', it can very easily be interpreted to mean "If you are not 100% fully and completely satisfied with your purchase, simply return it to us for a prompt replacement, or a refund of your purchase price." Would it make much more reason to you if they asked for a refund 'because we don't like the sound of the keys when we press them'?? The principle is the same. You offered a NO RISK, money back guarantee.
Some random thoughts:
1) Tell us the full EXACT wording of the guarantee that you offered and where it is noted (brochure, presentation, handout, etc.).
2) Tell us the full EXACT wording of any exlusions or modifications to this 'guarantee' and where they are located.
NOTE: If one place says "30 day no risk money back gaurantee", you cannot modify it by putting exlusions elsewhere (on the receipt that the customer doesn't see until after the committment for sale).
3) Who (title and position) was the person who placed the order for the day care??
4) Is this day care an independent company or a part of a chain??
5) Did the person placing the order tell you that he/she was authorized by 'the owner' to place orders for equipment?
6) Were you made aware that the day care did NOT have authority to place the order?
Though I personally feel that you have little or no legal basis for refusing their refund request, the answers to the above questions could affect your possible outcome.
Also, I would suggest that, in the future, you make the authorized person sign all documents (orders, delivery, amendments, etc.), including a statement that they have the authority to do so.
Finally, if your guarantee does indeed have limitations, you can't call it a 'no risk' guarantee.