Half of screen is black w/ colored stripes

Try to reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again. You will not lose any data by resetting, but it can cure some glitches.

If this does not help, setting it up as new device would be the next step:

Use iTunes to restore your iOS device to factory settings - Apple Support

If this does not work, the problem has to be hardware related and you'll have to get it serviced. If you're lucky, Apple only has to replace the screen. If the damage goes deeper, you'll have to pay the Out-Of-Service fee, to get your device replaced by a working unit.

iPhone - Contact Support - Apple Support

Screen repair service pricing
Repair and replacement costs depend on your iPhone model and your AppleCare product coverage. Apple will run a diagnostic test to determine whether your iPhone has experienced additional damage. If it has, or if it needs other repairs, you may need to pay an out-of-warranty service fee. Accidental damage isn't covered under the Apple One Year Limited Warranty.

Model	Screen repair cost
iPhone 6	$109
iPhone 6 Plus, iPhone 5s, iPhone 5c, iPhone 5	$129

Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing. Pricing and terms vary for service through an Apple Authorized Service Provider.

Out-of-warranty repair service
If your repair isn’t covered by Apple’s One Year Limited Warranty, AppleCare+, or AppleCare Protection Plan, your iPhone might be eligible for out-of-warranty service. For example, liquid damage isn’t covered by warranty but might be eligible for out-of-warranty service. Some damage isn’t eligible at all, for example if your device has been broken into multiple pieces. See Apple’s Repair Terms and Conditions for complete details.
Read Apple’s Repair Terms and Conditions

Model	Out-of-warranty service fee	Battery service*
iPhone 6 Plus	$329	$79 *available only if battery fails Apple’s diagnostic test
iPhone 6	$299
iPhone 5s, iPhone 5c, iPhone 5	$269
iPhone 4s	$199
iPhone 4, iPhone 3GS, iPhone 3G, Original iPhone	$149

Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing and may be less than the service fee listed above. Pricing and terms vary for service through an Apple Authorized Service Provider.

copied from Service Answer Center - iPhone

Basic Troubleshooting Steps when all else fails

- Quit the App by opening multi-tasking bar, and swiping the App upward to make it disappear. (For iOS 6 older, hold down the icon for the App for about 3-5 seconds, and then tap the red circle with the white minus sign.)

- Relaunch the App and try again.

- Restart the device. http://support.apple.com/kb/ht1430

- Reset the device. (Same article as above.)

- Reset All Settings (Settings > General > Reset > Reset All Settings)

- Restore from backup. http://support.apple.com/kb/ht1766 (If you don't have a backup, make one now, then skip to the next step.)

- Restore as new device. http://support.apple.com/kb/HT4137
For this step, do not re-download ANYTHING, and do not sign into your Apple ID.

- Test the issue after each step. If the last one does not resolve the issue, it is likely a hardware problem.