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Check the Downloads folder on your computer

The application is not in my recent downloads. As I download the zip file, it pops up there once it's finished, and then around 2 or 3 seconds later, it literally disappears. At this point I am not sure if it's a problem with the download and application itself, or my computer, since others are able to at least download and open the application.

(-1)
This is all I find in my downloads folder.

There might be an antivirus program on your computer removing it. It might be McAfee or Norton or something like that.
Open whatever antivirus you have and there should be a place where it lists the files it has removed.

I looked at all the possibilities in my antivirus program, including history and ways to stop blocking file downloads, but nothing is forthcoming, unfortunately. I wasn't able to add the file to pass through the antivirus check since the file doesn't exist in my laptop in the first place. I tried prematurely opening the file as it downloaded, but upon 'opening' the file, it just gives me a notice saying that my access request is denied. As far as my laptop is concerned apparently, the file does not exist. Thank you for your help so far; if it comes down to it I'll probably contact a tech support place to see what's up. 

It sounds like it's probably the antivirus. It says access denied when the file is gone. You might want to completely disable the antivirus and see what happens.
You could also try downloading with a different browser, but I don't think that'll make a difference.