I don't normally respond to these, but I was having the same problem and refuse to pay more for something because the system doesn't work.
The people I talked to on the phone were very nice, but not helpful. I received the same advise of "try a different browser" and "clear your cache/cookies". It is not our computers; I can only assume it's a hole in the website.
***Solution***
I downloaded the TurboTax App. Signed into my account. It loaded past the initial direct deposit step that would not load on the website. It would not let me digitally connect my bank account, but I was able to manually type in my bank account information. Total success in continuing through the final "sign and file" steps.
Hope this helps!
