The siren has a rechargeable battery in it, and eventually it will need to be replaced. Thus the replacement kit in a previous post. The battery is there to allow the siren to work if an unscrupulous person cuts the battery cable or otherwise cuts power to the siren.
When you let a modern low or no maintenance battery go dead, it's almost impossible to get it to recharge with one of the .75 amp or 1.25 amp battery tender type chargers. You need a lot more oomph to get the chemical reaction going, and I have successfully used a 10 amp regular battery charger in such a situation. Just be aware if using a regular charger that you can't just hook it up and walk away like a battery tender. It will need to be monitored to keep the battery from overheating.
Once the battery is showing a full charge, you will want to do a load test to make sure it's still good enough to rely on. Take it somewhere where they do load tests, or approximate it yourself if you have a good voltmeter. Remove the fuel pump fuse to keep the engine from starting, and with a voltmeter across the battery terminals crank the engine for 15 seconds with the starter while observing the voltage. If the voltage drops below 9.6 volts your battery is toast.
Jerry
Oh, btw, don't hook a charger larger than 5 amps to the battery tender harness. There is a 7.5 amp fuse in that harness.