Hi,
Thicker cables and a shorter run to the inverter may help.
Cleaning up the battery posts and the clamps may help.
A 750 watt may draw up to 75 amps from the battery, depending on how it is loaded. Be careful to make sure you don't end up with a dead starter battery.
Have you tried plugging the shore power cord into the inverter?
If the fridge has a compressor, it may want a start up surge of ten times the running watts. Without enough battery power that is not going to work well, particularly on a modified sine wave inverter. Most folks with compressor types look at a 1000 watt continuous pure sine wave inverter.