Hey I understand the whole husband-being-glued-to-the-PlayStation thing. He didn't listen when I asked for help cooking or cleaning and I could literally not get his attention with anything and that includes lingerie.

I think your husband may genuinely want to help you, but he really doesn't know what to do. If he's like my husband, his mother always did all that stuff for him and he really doesn't know what goes into keeping up a household and he couldn't do it all even if he tried. It's not a good feeling for a guy because he wants to take care of his household, which is evident when he says he's a sh***y husband.
So have a nice sit-down and make a list of chores that you can divvy up. You could even stick the list on the fridge so he has a reference. He may have fewer chores than you at first, but he'll get used to doing them and maybe you could both agree he will take on more as times goes on.
As far as the PlayStation goes, my opinion really depends on whether he has a job as well. If he does have a job, then when he comes home he probably needs a solid hour of gaming because it's how he relieves stress. It's the equivalent of you coming home and talking to him about your day. But also talk to him about it and let him know that you understand he needs to game but he also needs to limit it because you need his help.
So, like I said, let him game for an hour or so when he comes home and then maybe you both could agree that when the hour is up it's ok for you to come up to him and say you need his help so could he please stop gaming and help you.
This really does work, I assure you, but it'll take some time for him to get into the habit of it so unfortunately you're gonna need a lot of patience lol. It may feel like you're dealing with a teenager at first, but eventually he will get into the habit of helping you.
I don't have any kids but my mom is a teacher and when we were young, when she needed to grade papers and stuff then my dad would take us for a walk or have story time or something to occupy us. Perhaps your husband could do something similar so he's interacting with the kids and you have some peace while you try to grade and do your own homework.
Congrats on going back to school, BTW. That's awesome.

Good luck and let us know how you are doing!