Does your clock work at all? You really need tell us what the problem is so we’re not just guessing.
I would start by eyeballing the battery compartment and making sure that the contacts are not corroded. You can use a little nail file to file them clean to make sure you have good connections.
If you Google clock plus a few of those song titles you’ll get a few links to the company that makes those clocks… which are surprisingly expensive. Once you do the first googling you can also search eBay where there are some of these clocks listed for about half of retail… Which is still in my humble opinion bloody expensive.
I doubt you’ll be able to find a replacement movement… They probably had a bunch made for their various clocks… They are definitely non-standard.
Those clocks work with a standard "trigger movement". Getting the hands on is the bigger issue, because the original movements are specially made for the clocks. I have successfully used brass tubing to extend the hour and minute arbors for them.
If your issue is with the movement, you have a chance at fixing it. The electrical boards may be a harder problem if that's where the issue is.
That's an odd symptom, but these clocks do indeed use a standard 'trigger' movement for timekeeping, and Timesavers sells them. The only way to disassemble the clock is to start from the front, which means that you must pierce or remove some of the stick-on gold decor. These are difficult to work on.