Judging by the rusty, dirty appearance of that bottom bracket and the fact it's a "nutted" spindle, it's a low quality bottom bracket to begin with and now in very poor condition. I recommend removing and discarding it and replacing it with a suitable cartridge like a Shimano BB-UN54 or BB-UN55 in the right spindle length.

Apparently you have been able to remove the non-drive side lockring and adjustable cup. You will have to remove the drive-side fixed cup and that's almost always a lot tighter and requires a different special tool unless you can improvise. It might be worth the few dollars to have an LBS remove it. Remember the drive side is LEFT-hand threaded.