Can I use a 12v battery to power my 89W TV
Yes, you can. You need an inverter. The inverter might be 80% or more efficient, so if the TV actually consumes 89W then the inverter will draw 111W or about 9A from the battery. 

If you know the number of ampere-hours your battery holds, you can simply divide that by 9 and get the approximate run time. Car batteries are not designed for deep discharge and running them flat will truncate their useful life. 

For example, here is the specifications for the battery for my winter car- an Interstate MTP-91



It's 60ah, so it would run the TV for 6-7 hours to full discharge (when fully charged). If you use only the top 75% of the battery charge and it is fully charged, you can get about 5 hours. It's likely the TV uses much less than the nameplate consumption so you may get longer life. Easily checked with a device such as a Kill-a-watt.