With the stated use and results, you either have batteries that are diminished in capacity, an incorrect indicator, a very power robbing inverter or are running other loads that are not stated.
You have 380 AH of capacity with the four batteries. There is little possibility that an average LCD screen and a typical inverter can lower the voltage to 12 V with an hour of use. Typical inverter efficiency is 90+ %. Typical LCD screen is less than 100W. That is 1.2 amps (or less) at 120 V. Adjusting for 12V and allowing for inverter loss, amps = 12 amps. One hour of use 12 AH. Where did the other 180 AH's go?
I'd suggest that you break out a hand-held meter and get exact measurements of what your batteries are doing. Also, an inexpensive hydrometer will tell you their state of health (capacity).
You would also do well by changing batteries out for genuine deep-cycle batteries if you plan to do some off-grid camping. That is what others are using when they report multiple days of use from a set of batteries.
If your inverter is only used for entertainment devices and occasional laptop charging, you would definitely benefit by using a smaller inverter. If microwave, coffee maker, or hair dryer use is in your regimen, keep the 2000W inverter.
FWIW, I run a small residential fridge, all my entertainment devices, and charge electronics through a 1000W inverter, one 235 W panel, and 300 AH of batteries. If the sun shines, it's like perpetual motion. I also have typical 12 V loads but no 12v alarms, no furnace fan, and have all LED lights.