Yeah, don't quit. Yet.
You may have just gotten the bad luck of landing in an IT department that isn't newbie friendly. Because face it, that's what you are. Your monitor story is enlightening. Your manager went to the explanation that resulted the fastest in it not being your or her problem anymore. Dead pixels? Warranty it. She was frustrated because you spent all this time earnestly looking at the problem like you could fix it, when probably 30 seconds for her would have determined the least painful, least time consuming way to solve a problem. (She also probably has experience running warranties through, and having been on plenty of corporate software websites, that's not insignificant knowledge.) Hell the way you describe it, her answer may not even be the right answer. But maybe your boss is more interested in clearing out problems than actually solving them correctly.
And that tells me your department feels over worked, and yes, newbies can be an aggravation in that environment. I got irritated at our new hire today when a call came in at like 5:04 on her phone and she went "Oh, oh, oh, I just logged out of the call queue!" Well.....it's still ringing on your bloody phone, so ANSWER IT. But no, instead I went "Just let it fail over to me and I'll take it" even though it was after 5 and I had already clocked out. So I just took the call, over her trying to say she could take it.
Truth is, I was already worked up talking about another work issue (the fact we have zero boundaries with our customers so they'll call up and say shit like "Hey I just bought this new piece of software you've never heard of. Install it and set it up for me") so I was
already in a bad mood. Was it fair for me to get waspish with her? No. Was I able to realize that at the time? No.
Your boss likely has the same thing going on. Busy tech places are fully of people feeling overworked and patience is thin. Your department probably? deals with work-a-day in and out repetitive tech tasks, so small issues like this are swept under the rug so to speak just to get them out of the way.
It was already over my time limit but I really wanted to at least get that done but no dice. In the end, she raised her voice at me and asked me where I was and so on. I felt I had a good alibi but she her look is one of..idk. Not good. But also trying to look away to not show I feel.
Well, what are your overtime rules? It is not a good sign when you feel you need an alibi or your boss thinks you need one. That is a bad sign of them suspecting you as a layabout.
Hell I volunteered to do an event that they needed me in where my other boss vouched for me to be good (i'm wearing a mascot outfit. Out IT dept at our school does IT and Media/Events) and I feel good about it. But the tech side..no.
Note the complete difference in attitude between your two bosses. It comes as no surprise to me that your "other boss" on the non-tech side has no issues with you.
Sorry I don't have any solutions to you. In truth it just takes grit and a willingness to accept stress, pretty much what Vector is getting at. In some ways learning to survive work as an adult is like trying to survive highschool as a teen. You lack the control of your surroundings but you gotta be there anyways, whether by law or so you can eat or so you can become a grown ass man.
What really did it for me was pride, if nothing else. I refused to feel weak-willed or to cave to pressure. I focused on my shit and castigated myself for not meeting my own standards when I failed. My bosses currently say "Look man, we don't ever need to come down on you for not working/screwing up. You come down on yourself plenty." Pride enough to say "Look man, I know I'm new and I don't know shit about shit. But don't look down on me for it,
work with me." If you both lack the knowledge and skills to do your job and well and the backbone to show you care, people will walk all over you. They will treat you like a whipping boy. They will vent their unpleasant emotions on you because they don't respect you. The fact your boss is effectively challenging you to justify yourself and you look away....you're sending all the wrong signals, like you've got something to hide or you're too weak to defend yourself.
You can't control your coworkers. You can't control the flow of business. The only thing you can control is yourself and how you respond to things. I say this with caution but....maybe get a little angry. Get a little intense. Get some testosterone flowing.
Attack your work. You want respect? You have to earn it in their eyes, they won't simply give it to you because you're nice. Tech is a job where people need to know things and do things and eventually do them quickly and handle complications. If you want respect you have to meet those criteria. Because you may not get fired...but if you ever want to feel good about yourself at work, you have to rise to the occasion.
PS - Irony. In the middle of writing this post my mom calls to talk about her retirement plans, her on-going war of words with a sexist, mean-spirited department head she's been fighting with for years, her new attitude of "you know what? FUCK WORK." Basically the polar opposite of this conversation here. For decades she's had a protestant work ethic to the point she didn't know how to let go because she took her job too seriously. And she just finally figured it out I think.
Your problem seems to be you are unable to grab hold. Hopefully you can experience a revelation too.