#1: HTC Droid Incredible
 Error: it's screen has a blue hue to it, and sometimes what looks like general color distortion - installing Screen Adjuster only helped a tiny bit. Anyone know how I can determine if this is a software problem or a damaged GPU?

This sounds like a hardware issue. I looked around, and it seems to indicate a potentially loose LCD ribbon...? If the colors changes when shaked, it's likely to be the cause. (Don't shake too hard, since you might cause permanent damage!)

Source

#2: HTC EVO 4G
 Error: It cannot charge it's battery, I assume the MicroUSB port is damaged. Is it possible to replace it's port?

It's always possible! Of course, the question is whether it's hard or not...

Looking at the phone's replacement parts, it *might* be fixable if you're really good at soldering. It does have very tiny pins though, so beware: Replacement Part for USB port

#3: HTC Thunderbolt
Error: It randomly reboots. How can I tell if this is damaged hardware or a software issue? Also, it has a smaller HTC HD7 battery taped into it, if that could be an issue.

All three have been reset.

If you are able to, you will want to enable the Android Developer Mode. See this guide for some steps to do that! (Not sure if it's too new for the phone or not, but it should be similar...)

If you can achieve that, and successfully connect the phone to your computer, I can help you out with the next steps to get the logs from the phone. Those logs will really help with understanding what is wrong with the phone.

#1: Well, no, shaking doesn't seem to affect it. Maybe I should take it apart and look at the connector? Any other possibilities?

Not that I know of - it almost certainly sounds like a display issue to me. The only other option is to replace, so there's that.

#2: Walp, that's about all there is to it, I'll look into replacing it. It's a shame it doesn't happen to have a seperate charging board like say the HTC 8X!

You should tell that to my other devices, all with SMT soldered on USB ports!

#3: Yup, Developer Mode now enabled. What next?

So you should do the following:
Installing ADB

• Find the drivers for your phone. You should look for general USB drivers. If there's a developer driver for your phone, install that as well.
• Install ADB. You can either get it from the official Android SDK (found here), or if you're more adventurous, get it from here. (The latter link is for Windows users. For Linux users, you can try here for some information about getting ADB directly.)
• Locate your ADB program. On Windows, it's called adb.exe, if you show extensions. For everything else, it's simply a file called adb. Note the folder where ADB resides. On Linux, if you are able to install ADB to your system, skip this step.
• Open a terminal/command prompt, and change directory into your adb directory. (You would usually use a command like cd C:\ADB_INSTALL_DIR or cd ~/adb_install_dir to do this.) On Linux, if you are able to install ADB to your system, skip this step.
• Now run adb: adb on Windows (or if you installed it to your system on Linux), ./adb otherwise (Mac/Linux). Remember which one you used - we'll be referring to the program as adb from now on.
• If you see a lot of help output, yay! You got it! If you get command not found or The system cannot find the path specified, let me know.

Phone Debugging
At this point, you should have ADB working in order to continue on to the following steps.

• Ensure Developer Mode is enabled on your phone, then plug your phone into your computer.
• Run: adb devices - on Linux, you may need to add a sudo or su -c before that command for it to work.
• On newer devices/OSes, you may get a prompt from your phone to allow debugging. Simply tap "Yes" or "Allow" to enable USB debugging.
• You should see your device in the list. If not, try running it again.
• Now, type the following: adb logcat > logfile.txt - this will start dumping logs from the phone to your computer.
• Use the phone normally, until it crashes.
• Once it crashes, the command should exit. Immediately after that, run: adb logcat > logfile-postcrash.txt. If it doesn't work the first time, keep trying until it works.
• Now you can examine both logs to see if there's any software issues that might be causing this! Feel free to post the logs here for everyone to look at!

Good luck!

EDIT: Please ignore this really weird thing at the end, it's an SMF bug: [/list]

Update on the Droid Incredible: It's not booting anymore. I accidentally deleted the launcher, though I don't know if that'd cause it to stay at the Droid splash screen forever, I think it should cause it to show a black screen with the notification bar with android actually running. I'm assuming the OS is corrupt somehow, so my only hope is to reflash the OS while it cannot boot. Noone can tell me how to do this - I've already looked on Google - but anyone is welcome to post if they want.