Wow, you contacted them and they said they didn't know. That is kinda said, since that is what they are paid to do. Fix tech issues. Anyway....
OK Well it sounds like there may have been some bad stuff installed onto the device. The best way to know if that is why for sure is to turn the phone off, pull the battery for about a minute, then put it back in but don't turn it on just yet. First try charging it while the phone is totally turned off and see if it shows as charging. If not, try the cord on another device and see if it works with that. If it doesn't, you need a new cord, if it does then it could be the battery that needs replacing or the motherboard (which is where the port is attached) that would be a bit more work, so start with the cord.
As to trying to get it to turn on. Well as long as it has a little charge, as stated above, turn it off, pull the battery, put it back in a minute later and then do not turn it back on just yet. Follow the instructions below to get the phone into "Safe Mode" and see if it will load. If it does, then you have an app or other software on the device that is causing your problems. You will need to remove said app/software and then restart the phone.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable safe mode, simply repeat the steps above, and you should see "Safe Mode: Off" rather than On.