I have an iPhone 7 Plus, running iOS 10.3.1, which is says is up to date.

When I open the Camera app, the Time-Lapse, Slo-Mo, and Pano modes work. However the Video, Photo, Portrait, and Square modes do not work with the front lens. All I get is a either a black screen or a very blurred image of what the lens had seen on one of the modes that worked. The app will not take a photo of even the blurred image. However, I can use the "selfie" lens and it works.

Additionally, my USAA app, which uses the front camera to capture images of checks being deposited, works fine. So I do not think this is a hardware issue.

I have turned my phone off and on, done a soft reset, a hard reset, and reset all settings. The only things I haven't done yet is do a factory-reset or go to the Apple Store.

Any ideas?

My next step would be a trip to the Apple Store.

I'd do a factory reset first. It's pretty painless when you backup just prior, and it's probably what the store will do with you sitting there so you might as well do it on your time.

Factory reset first.

If that doesn't work, uninstall any app that uses the camera one by one. If you go into settings, you will be able to see what apps have permission to access the camera.

If those don't work take it to the Apple Store. But they are likely going to ask you to do those steps there anyways if you haven't already done them.

Apple Store. Great thing about having an iPhone. And they'll likely fix for free

I had the same problem with mine and had to do a full reset (Erase All Content and Settings) and restore from an iCloud backup to fix it. I've had zero issues since doing that a few months ago.