I have bought a new replacement from hcqs.com.cn and followed the steps below to fix it:
Step 1. You will have to disassemble your Note 3 first.
Step 2. Once your Note 3 has been disassembled, take a screw drive and push on one of the holes on the top-right of your Galaxy Note 3 as shown below. This will make your screen digitizer pop out of the front.
Step 3. Once you have a small gap that’s formed, take a thin, plastic knife and slide it towards the bottom. Do this until the whole screen digitizer comes off.
Step 4. Pull the film on your brand, new Note 3 screen digitizer assembly.
Make sure you cut the end of the tape that’s attached to the LCD flex cable. This will allow your LCD connector to move freely so you can easily connect it. I found out the hard way (as shown in video) that leaving this tape on will cause headaches when you try to connect the LCD connector later.
Step 5. Make sure you have the home button on the new screen digitizer assembly. Then put it on top of your frame while making sure the LCD connector goes through the hole.
Step 6. Once the screen is back on, the rest is easy as you just have to reassemble the Note 3 backwards. If you have trouble, watch the latter part of my disassembly/assembly video while you do it.
Step 7. Before you put the screws back on, try putting the battery back on and make sure your screen, touchscreen, wifi, bluetooth, and other sensors are working.