Is it possible that I am blacklisted with a company I never worked for?

2 years ago I worked for a company right out of college and got let go after about 2 months of working for them. I never really found out why I was terminated. To my knowledge I did nothing wrong and I found out later that they had also terminated another employee who had the same title and had been hired the same day as me. Anyway fast forward to today, I don’t want to work for them again but I cannot access their website from my computer. However I can from other computers in my house.(so random) There is another company across the street from them that is in the same business. (their competition and much larger company) I have filled out applications with them, even the easy ones that I know I can get. At least 15 different times, they have never called me back or even acknowledged my application. I’ve pretty much given up on them because I figure its a waste of time. Anyway, I wanted to know is it possible that I could be blacklisted with them from the company across the street? Oh, and this is a government type job.