TC = FC + CC. Always. With a CYA of 70-80, you need to be shocking up to 20ppm. Adding 4 big jugs would have added 45ppm! Way too much! So, what is really happening in your pool is that you have so much chlorine, that you are probably bleaching out the DPD test and it appears that you have none!

Don't add anymore chlorine at this point. Use a dilution test to see if you can get a better reading. More about that here: Testing Without a Good Kit

Your pH test will be inaccurate with high chlorine. But, typically with high chlorine, you get a falsely high pH. So, I'm going to suggest going ahead and adding a half a box of Borax slowly to the skimmer while the pump is running.

You do not need a new filter, but your pump is WAY oversized for your small pool. We see this a lot. When a pump is too big, it forces stuff through the sand bed without filter it out well. Thus, it can take a long time to clear a pool.

Repost with the dilution test results. Also, if you can, order that K-1515 add-on kit I mentioned above.