First a quick explanation of how the freezer may have failed. A surge suppressor will protect part of the fridge/freezer from problems. The controls and the electronics it can protect. But it does not protect the compressor.
The compressor is running and under normal circumstances it runs for longer time period and then is off for a longer time period too. During the long off period the pressure in the compressor bleeds off so the compressor is starting against a fairly light load comparatively. If the power blinks the compressor stops but then the power comes back on before the compressor has a chance to bleed its pressure down. The motor isn't strong enough to start against this high load. Now the compressor tries to start for about 30 to 45 seconds. During this time the winding in the compressor is getting warmer. Eventually the thermal overload outside the compressor trips and kills the power. Normally the thermal overload takes enough time for the pressure to bleed down that by the time it cools down enough to reset the compressor is ready to start. No one ever knows the compressor was locked solid for a bit because everything resets in 5 or 10 minutes.
Now this can lead to multiple failure modes. 1. If the power bounces repeated for a time slightly less the thermal overload trip each cycle gets the winding inside the compressor hotter while the thermal overload being outside cools faster. The compressor may even manage to start while the cycles are happening but the power goes out again and it stops. If those cycles continue at the right pace the winding gets hotter till it burns up. 2. The thermal overload fuses in the on condition for some reason so now the compressor becomes a resistance heater because the compressor can't start. There again the cycling makes this more likely to happen. 3 in cheaper design compressor systems the relay that runs the compressor and the thermal overload are part of the same mechanical system. The contacts in the main relay fuse and the thermal load can't open them so there again the winding burns up. It is bad luck or protection system failures that take out the compressor. And no surge suppressor will will protect against this. An inverter and battery would because then the power should never blink repeatedly to the compressor.
Now a quick comment on power calculations. A typical household to light commercial compressor unit will be rated between 1/6 and 3/4 of a horsepower. But remember other things can be running at the same time. In a large side by side 4 fan motors, ice maker motor and door lights. Older machines the door light bulbs draw 40 watts each. Also the controls draw a bit of power. The other major power draw is the defrosters but they typically only run while the compressor is off so ignore them typically in the math. So if the compressor is say 1/2 hp and the rest adds another 1/4 hp worth of electric draw that is what you are working with. 3/4 hp = 560 watts But this still isn't enough to size the inverter. The problem is that the surge electric draw is far larger on starting. So your inverter needs to cover both run and surge needs.
Now there is another option I have a newer chest freezer with dead compressor so I have been looking at options. If I put a 12/24 DC volt compressor in it then I can avoid the expense of a full DC unit while getting its benefits. Figuring it is going to take a bit over $350 for the compressor, electronic controller, gas and other materials.(doable if I can do my own work so there is no other expense(I have most of the tools and skills needed) It is marginal as my freezer is too large to match the compressor's volume rating. But it is high end with great insulation so can I push it a bit more? What about building an insulated case around the freezer and moving condenser to outside it? By doing DC as the primary I would be all set for solar power but a large switching supply and the system would run on AC too. Here is the link to the compressor. The electronic controller costs about as much as the compressor.
If I did it there are 3 other dream systems I would like to try to set up to include at a future date. 1. Completely passive solar thermal powered refrigeration system so the DC/mechanical system only rarely ran rarely. 2 Wind powered compressor dumping heat else where and then blowing small quantities of really high pressure air into the freezer allowing for air powered cooling. 3. a suction line run diagonally thru the insulation to allow freeze drying without a fancy freeze drier. A simply paint pot or pressure cooker in the freezer and cold for the cold chamber with a hose connecting to the inside wall. Outside the freezer another pot and the vacuum pump.