Seems like an aftermarket alarm system was added to your car.
However, the owner must have not had the money, or the shop didn't have the knowledge, to connect the alarm system to the central locking system.

You can have this done fairly easily, and it wouldn't be too expensive, considering you already have the unit.

"II" on the remote is for extra options.

See if the remote works... arm the car (blink the lights once), and then try and open an unlocked door to see what happens... if nothing, then further try and start the car.

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2006 E350 w/ 155k miles (Daily Driver)

Previous:
1993 300E 3.2L Sedan w/ close to about 300k miles
2003 E500 Brilliant Silver (Had 217k miles when totalled!)
1989 300E with 289,000 miles (had for <1 yr while in HI)
03 CLK 500 cabrio (Mom's)
2006 C230k (Dad's)
1999 S420 (Mom's/Dad's)
2000 C230k Sport sedans
2001 CLK320 Cabrio (Mom's)
1995 C280 My First Mercedes-Benz... (155k miles. EXCEPTIONAL AUTOMOBILE. Was Very hard to let go of!)