I don't have any current, relevant experience to offer. Sorry, I can't help with specific advice. However I was the hiring manager for many hardware EEs a while ago. Here's my take:
1) If you had a degree from a well respected institution (not just accredited, well respected), then I would assume that you have met some minimum standards for passing university level courses. If that institution was Caltech, MIT, Princeton, etc. then I would assume that you were outstanding at the high school level, probably already doing college work. I might select you above others to interview.
2) If you were a graduate from a low quality institution, that I had experience with interviewing graduates from (Heald Collage comes to mind), then I would suspect that you didn't have the fundamental, background education that we needed (a very high tech company, BTW). I would probably select you to interview if I saw that you had other applicable experience, interesting projects, etc. Otherwise I would probably pass over you. Yes, I know it might be unfair, but I'm a Bayesian in practice (google that if you don't understand, it's worth knowing).
3) In any case (this is the important part!), if I do interview you, you will probably get the same technical questions that I ask everyone. It is what you actually know that counts. I have interviewed people from famous institutions that really didn't have fundamental understanding of their field and I have interviewed people from lesser institutions that had really good understanding of how circuits really work. I have been surprised in both directions.
I think it is a two step process, get an interview and then convince people that you know the subject. I think this is much more true in technical fields than employment in general. At good companies BS is detected early and not tolerated. OTOH talent will succeed in the end.
Your first challenge is to get a good education, however you can, wherever you can. Then you will have something to show off when people ask. I'm not sure that, in the end, the real question is "is this institution respected?", I think it's "can they teach me what I really need to know?". However, there is a reason that famous institutions garner respect. If you have graduated from Caltech, MIT, or Princeton with a physical science degree, I know that you know calculus. If you graduated from Heald, DeVry, etc. then you may need to show me that.