Have you tried to run an SMC reset? Try that first and then report back! https://support.apple.com/en-us/HT201295 (while powered off, connect to power, then hold left side, shift, control, and option, then press the power button. wait 5 seconds (you might see the mag-safe connector go from green to orange, then green again) then try again)

Sounds like there is either an imbalance to the fan or something is damaged inside it. Regardless you’re likely easier to replace that fan.

If the traces are okay take a peek at the flex cables and make sure they're all intact and connected on the display properly. I, sadly, just replaced the battery in my iPhone 5S and managed to shear off the LVDS/LCD Cable, it was still attached with the copper grounding sticker so unless I had tugged on that one a bit, I'd have been scratching my head for a while. The device being seen by iTunes is a good thing, but only shows that the logic board is functional. interesting way to see if its just the LCD, try pressing and holding the Sleep/Wake/Power Button for about 5 long seconds and then swipe as if the slide to power off had shown up on the screen, if the device disappears from iTunes (as if it were disconnected) then you know its the LCD. Finally it could be the backlight filter is bad, using a bright light source see if you can make out video on the screen at all. if you have any visible image when you hit the home button then the backlight or the filter could have failed.

You would be able to do what you're looking for, but you may have to install an OS on the external drive for Time Machine to recognize that as a destination. Its not hard to do honestly, but again you'll have to install the OS. Simplest way to do that is connect the drive to the computer and either using the recovery partition or downloading the macOS installer from the AppStore onto the system you'll be able to target the external drive to install the OS (you may even have the option of restoring a Time Machine backup directly from the recovery partition. If your Time Machine backup is of one of the newer versions of macOS you could be able to boot the computer from the Time Machine backup directly and complete some of the steps outlined above. Ultimately Time Machine is just going to ask where it should restore the backup and I see no reason why an external disk formatted as HFS+ wouldn't show up in said listing. The only caveat I'd look out for is the inherent risk of using an external drive to boot the...

In the past i'd done a similar trick to get better wi-fi in another mac. I recall buying the wifi/bluetooth module for a G5 or MacPro and installing that in a MacBook to get the 802.11 N setup that wasn't a part of that current generation. What i'd do is take a look at the configuration of the card you have currently in the computer. It could be useful to take out the unit you have and take a good picture then re-install and compare your photo to that of the one you're looking at. The software is all included as a part of the macOS so drivers aren't an issue for most cases. Count the number of pins you can see and compare the notches for the screw and the slot. If they match up its pretty reasonable that it would work. A very major word of caution. If there is a voltage issue on the card, either requiring too much or needing much less power there is a risk of causing damage to the card, slot, or main logic board of your system. The final note is that in the cases of people doing things like this you may...

You mentioned you replaced the power button and volume buttons. It could be that cable is being depressed and something is causing the device to enter recovery mode. Its a pain, but if you can get back into the device and re-seat those cable connections on the logic board that could solve the issue, verify the buttons click freely and aren't spongy at all before trying to replace them again.

Could you be a bit more specific? Do you know what was happening leading up to the current problem? I am going to write all of the following assuming you have a mechanical Hard disk, NOT and SSD. If you have an SSD some of the following information will not apply (such as an audible verification of the device working) I am going to assume that when you attempt to power on you're still hearing the chime, which means the Logic Board and RAM are checking out okay. If you get a grey screen that means the video card is also fine (a sub segment of the Logic Board) and if you get to a flashing folder icon with a question mark then you have one of a few different possibilities. First and easiest check would be to hold down the option key as you are trying to power the system on. If you see a blank grey screen with an icon showing what looks like a Hard Disk and the words Recovery HD XX.XX where the XX is what version of the macOS you have/had installed then you may have something going on with your main partition...

As you're going to be ordering a whole replacement display assembly it is safe to say that the sensors for 3D Touch will be a part of the repair. They are embedded with the LCD and Digitizer as another layer. If you're feeling curious, get a high intensity light and a decent magnifying glass and look at the LCD when off you may see a series of fine lines that make up both the digitizer and the force sensor on the LCD. If you'd like more detail, check out iFixit's teardown of the iPhone 6S and 6S+ for some great photos.

While you did clean the fans that doesn't mean that the floating bearing isn't failed/ing. You're probably going to need to replace one or both of the fans in that system. I know it doesn't help you now, but in the future, try to remember to go for the cheapest suspected parts first. If you replace a fan and it's not needed, its a smaller hit to the wallet for something that won't hurt the system all that much. If I recall properly, the "left" fan is what you're probably going to want to order as that is how Apple labels the fans on that system. Good Luck!

Vacuum cleaners generate a ridiculous amount of static. and can potentially harm a computer. They make special vacuum cleaners for electronics that don't generate static and don't hurt the components. As for rdklinc's statements, don't just go mad with the compressed air. short bursts from the can are preferred. while it is fun to blast till your hand freezes from the expanding gasses in the can, you could do some harm to the components if you blast them too much. But like he said. Top case off, Hold fan with finger (you grounded yourself first right?) and short bursts on the fan. It can be a good idea to remove the fan to get any accumulated cruft off the heat-sync too, but it isn't really required.