Nexus 7 tablet (original model) stuck in Safe mode; no way out?
I had the same problem. Spent a night to fix it. First i thought it to be a software issue.. browsed and tried infinite fixes. I tried re seating flex cable that connects the volume buttons and the motherboard.I tries to factory reset through boot loader. Thought of flashing a different ROM. Dint work out for me. 

Here is what worked for me.


Open the back panel of the tablet.
https://www.ifixit.com/Guide/Nexus+7+Power+%26+Volume+Button+Cable+Replacement/9926
Flip up the retaining flap on the 'power and volume button ribbon cable' connecting to the mother board. DO NOT PULL OUT THE CABLE NOW.   Be ready to pull out the cable.


3.Press the power button to switch on your tablet.

4.The moment you see Google logo, pull out 'power and volume button ribbon cable'. This will disconnect volume down key, which forces the tablet into bootloader.

5.Now the tablet is ON in normal mode. 

6.Plug the 'power and volume button ribbon cable' into its mother board socket.

7.Close the panel and enjoy using your tablet.

Be very careful with 'power and volume button ribbon cable'. A slight twist or bend will short the connections inside the cable.

P.S : After powering on, Try not to switch off the tablet. The volume down key might malfunction again and your tablet might go back to boot loader. Charge it before the battery dies out. In worst case, you'll have to repeat the above steps again. Messing with the power keys cable is not always a good idea :D

The volume down key and power key combination lets you to go into boot loader. So when volume down key is malfunctioning, your tablet might go for a toss. This could be for various reasons ,

a.Volume key is abused
b. volume key cable is damaged
c. Mother board is unable to supply enough power to volume keys.
d. volume keys socket in the mother board is damaged.