When you're working for a corporation, none of that matters. The only place it might is a "ma and pa shop" or an ethical NPO. Sad but true.
I do indeed know what you're going through though, what you're thinking and feeling and it's only been a week. I hope you land on your feet. I went through a period of prolonged unemployment that damn near broke me mentally and emotionally. Applying for all these "survival" jobs and being told, if I was "lucky" enough to be told anything, that I was over-qualified, they'd rather hire someone with less experience that they could realistically expect to stay longer because I'd leave for a better offer as soon as I got one, etc, etc,.
I read a study a year or so back that said having no job is mentally healthier than having a bad job. I completely and utterly disagree with that.