I'm not sure what's going on here, but that's not the way a Bobcat, especially a 773 works. First of all, are we sure we're talking about a 773? You note it's a 2008, they stopped making the 773 in 2002, by 2008 Bobcat was producing the S185. Aside from that, depending on what model we're working with, assuming it's a G series or later, when you first power up the ignition, even before you start it, you should hear one long beep from the alarm, just one long beep, not constant. That's the main controller (computer) doing a system test and also lets you know the alarm is working.
Once you start it, no LED's are lit up on the BICS panel until you drop the seat bar, then the seat bar LED light comes on and stays lit. When you push the "Press to Operate" button, then the lift/tilt and traction LED lights come on and stay lit. Once you start the engine and begin operation, if there's a fault that the main controller is seeing you will hear three short beeps from the alarm to alert you, not a constant beep. That's the way a Bobcat is supposed to work, if yours is doing things differently than what I've noted then there's something seriously flipped out about your machine.