When hilling up you don't want to bury the entire plant. Leave the top few leaves exposed and then add new soil as they grow. You really want to do this as the plant is growing, adding soil, leaves,
compost, hay, etc a bit at a time. Burying older established plants doesn't always result in more potatoes. Once the stems have developed, had exposure to sunlight, and developed fibers for strength they are stems and wont grow more roots and thus potatoes even if you cover them. For these towers to really work you have to keep burying the new growth. When they're really going strong I add more cover material every couple of days. Lots of these towers really just grow potatoes on the bottom 6-10 inches and nothing above that. Mostly because it's not as simple as the internet makes it seem.
I've tried different tower methods but these days don't bother with anything more than about 2 ft high. Higher never seemed to increase my yields and was just more work for almost no gain. I only 'tower' the late season varieties. Potatoes just like tomatoes have determinate and indeterminate types. Only the indeterminate types will grow potatoes all the way up the stem. The determinates (which many early varieties are) will set new potato buds all at the same time and once they are done it doesn't matter how much more you hill them up...you may get more roots along the stem but there will be no more new potatoes.
I'm not sure if a completely buried potato plant will resprout and even if it does I don't think your chances of getting a tower of potatoes is good. If I was you I'd dig down and see if there is anything surviving under all that soil and comfery. If you do find the original plant expose the tops and let them grow out from that level. I wouldn't try to keep burying them any more at this point.