Ok, thanks for the photo.
You have a frog type battery.
I also have one of these.
You must proceed with caution when working on the battery as it could be still working and fully charged
but just have an internal fault.
If you do not feel confident to proceed I suggest you find an electrical professional to check it out.
Without opening the battery you can do the following:
From what you have described so far I do not think the fuses are blown as the monitor still lights after charging. I removed my main battery fuse and the monitor goes dead so yours has to be intact if the monitor lights up.
It should have 2 fuse holders on the bottom of the case, one small one for the charging circuit located nearest the rear handle and one large one for the battery output right by the charging socket.
I suggest you remove the fuses one at a time and clean the metal end caps on the fuse with a kitchen scourer then refit it back into the holder several times to clean the fuse holder connectors.
Fit the battery back onto the battery cradle on the bike several times to clean the 2 connectors on the battery and the cradle.
Switch on and see if it makes any difference, if it does not make any difference then you will have to get inside the battery.
If need be, you can get inside the case by removing the 5 screws in the bottom of the case and take the top off but the monitor printed circuit boards is wired to the top case so you have to be careful not to pull on the wires when you remove it.
After opening it up all you can do is visually inspect the solder joints of all the wires on the fuse holders and connectors, carefully give them a wiggle to see if they are all sound.
I am afraid without a multimeter that is all you can try for now.