Replacing the batteries was a good idea. Replacing the batteries is inexpensive, and now you know that the problem isn't the batteries. However, going forward, you have to go deeper into the system to fix the problem.
I looked for the manual too, but I couldn't find anything legitimate.
This is an old panel. The rest of the system is old also. The problem could be with the panel, or it could be with the rest of the system in the building. Batteries are really just a small part of the whole system.
All electronics age and goes bad over time. Capacitors dry out, carbon resistors slowly change value as they stay warm, plastic that's holding parts or being used for insulation gets hard and brittle, tarnish builds up on contacts - making the contacts unreliable, etc. Over time, all electronics will suffer the same fate.
When there's something wrong with the electronics of the fire alarm panel, the trouble buzzer will turn on. As far as what's causing the trouble buzzer to sound off, something outside the panel could be the cause. If a smoke detector has come loose, for instance, that would be "Trouble with the Fire Alarm System", and the trouble buzzer will sound off with that. Maybe there's water that is causing a ground fault. On older panels, if there isn't a separate "Ground Fault Light", water could be a source of trouble. There are lots of fire alarm devices all over the building, and there is lots of wire connecting everything together. Basically, the trouble problem could be anywhere.
Then again, the issue here is that the panel is old, and not supported by the manufacturer anymore. In essence, you can't count on any support from the manufacturer to make sure the panel is going to "Detect Fires and Warn People".
You might be able to find someone with a manual so you can fix the panel. This is assuming, of course, that the panel is bad and not something wrong elsewhere in the building. But fixing the panel means finding parts, which aren't being made anymore. The best you can do is to either find used parts (this is a life safety issue; do you want to bet your life that used parts are going to protect you?) or else reconditioned parts. Again, this is a life safety issue.
Replace the Panel
Right now, the panel may or may not be bad. My recommendation, though, is that rather than spending a lot of time trying to fix a very old panel that could go bad again sometime soon, replace the panel with a new one. Then you'll know that the panel is good.
If the trouble is still on the panel, you'll know that there's trouble somewhere else in the building. I've fixed a lot of fire alarm systems. I've found that fixing the system in the building is much easier when I know the panel is working. You have to start somewhere, and replacing an old panel is a good place to start.