The machine should still boot with the power adapter plugged in even though the battery is bad, although, if the battery has been allowed to drain to nothing you may have problems. It will not boot with the battery out and the power supply plugged in. The psu unit for the Titanium and later Alu models is the same wattage - 65w so that should still work okay.
Try resetting the power management unit - hold the power key down for at least 6 seconds, let go then press once, if it still doesn't boot, reset the PMU from the logic board. The PMU on the logic board can be reset by bridging the two small pads with a flat bladed screwdriver. This is located on the logic board just above the track pad area to the left of the optical drive. There's a cable that runs along this area look there for the 3 sets of two pads, separated by a fine white line. There's 3 sets of 2 pads, one resets the PMU, one resets the PRAM and one allows you to boot the machine without having the top-plate and power button installed.
I'll email you some information that will help you locate these areas.
Try resetting the power management unit - hold the power key down for at least 6 seconds, let go then press once, if it still doesn't boot, reset the PMU from the logic board. The PMU on the logic board can be reset by bridging the two small pads with a flat bladed screwdriver. This is located on the logic board just above the track pad area to the left of the optical drive. There's a cable that runs along this area look there for the 3 sets of two pads, separated by a fine white line. There's 3 sets of 2 pads, one resets the PMU, one resets the PRAM and one allows you to boot the machine without having the top-plate and power button installed.
I'll email you some information that will help you locate these areas.