Let me start by saying congratulations! You have purchased a set of one of my all-time favorite speakers. They have an amazing ability to create an incredibly wide and deep sound stage. They are also great speakers for classical, acoustic, etc music.
I'm quite familiar with these speakers. I've got hands-on time with both the DCM TimeWindow 1 and the 1a. The grill cloth sock on the outside of the speaker is removable. Depending on if it is still the original, you should be able to gently slide it to the top or the bottom. This will allow you to visually inspect the drivers for obvious physical damage. You are completely correct in saying the glue is super hard, and very much so a PITA to work with. When I listen with my head very close to the speaker, I can make out the sound that each individual driver is producing. You should be able to verify which drivers are working by slowly moving your head around in front of the driver locations on the baffles. After that, I would recommend removing the nut from the bottom of the speakers, as there is a long threaded rod that runs down the center of the TimeWindow 1a that holds the top and bottom plates on. With the nut and threaded rod removed you should be able to remove the end caps and inspect the crossover for damage. You should also be able to look at the wiring for the drivers from the rear with the end caps off.
I have seen a few threads about purchasing new replacement drivers, I know there are some close replacements to be had on the internet. There are also quite a few people out there with TimeWindows that are too rough or too destroyed to listen to, so you might get lucky and find someone parting out a set on ePrey.
Let me know if you have any questions about how to set them up. Depending on your room size and layout, as well as the type of music you listen to, the ideal room positioning varies.
Driven with good, clean power these speakers can produce amazing sound. Listening to Adele or Diana Krall on a set of TimeWindows is nothing short of breathtaking.
EDIT: To address your concerns about the Onk receiver, I have used quite a few different receivers and amps with the TimeWindows. They definitely respond best to clean power, but I think your Onkyo receiver should be putting out more than enough in 2 channel operation for the TimeWindows to sing. The TimeWindows 1a's (if my memory is correct) are 89db/w sensitive, which means that they aren't going to be nearly as efficient as a set of Klipsch speakers for instance. I find that 80w+ is enough to get them to perform great. I would recommend that you make sure your receiver is set for 2 channel operation, to give as much headroom to the front L/R amp sections as possible. Additionally, depending on if you are using a subwoofer or not, you should set the L/R to receive a full range signal (set the L/R to Large). If you are able to set the receiver to a 'Pure Direct' mode or something equivalent, that would help.