An analogy to towing companies is tempting but misplaced, since towing is a statutorily-authorized and regulated activity (e.g. RCW 46.55). You therefore cannot just charge an arbitrary storage fee for uncollected equipment, and it is highly unlikely that there is any provision in the contract which authorizes you to charge for storage. The question is why you think you think they are responsible for picking up the excavator – presumably there is a clause in the contract that says that they will pick it up. Assuming that the contract doesn't say much, then your recourse would reside in the fact of their equipment trespassing on your property. You would need to officially withdraw permission for their equipment to be on your property (since you gave it in the first place). They would have a reasonable time to retrieve their goods, and if they don't do so, you would have a basis for suing them for damages. Also, the worst thing you could do is forcibly keeping their key until they pay you a storage fee: you'd need a court-ordered award, to get anything from them.
The Connecticut towing law is here. Note that in order to call a towing company to get the equipment towed (if that's even possible), there has to be "conspicuous signage" warning of the possibility of towing "on such private commercial property"; but an overriding consideration is that you may tow if the vehicle is left for forty-eight or more hours. Two points to be noted are that although the law refers to "An owner or lessee of private property", the signage requirement implies that the property has to be commercial, not residential (this limitation to "private commercial property" is repeated in the statute, indicating a legislative intent to restrict the legal towing permission to commercial property).
The law refers to "motor vehicles", but it is not clear whether an excavator counts as a "motor vehicle" (defined in para 54 of the definitions section). Although an excavator is a "vehicle propelled or drawn by any nonmuscular power", exceptions are carved out for agricultural tractors, farm implements, and "and any other vehicle not suitable for operation on a highway", which I think reasonably means that an excavator is not a motor vehicle. So since the towing statute does not authorize towing of something that is not a motor vehicle, that would not seem to be an option in this case (even if there were signage, and this is commercial property).
And calling a towing company would only get the item removed from your property, but would not authorize you to collect a storage fee (the towing company can only do so after the police have been notified, which they must do withing 2 hours).
