Guide to troubleshooting
First things are the senses: sight, smell (if it's a fresh failure) and touch. Use a strong light and loupe to check for cracked chips, black smoke marks or cold joints.
Press on the board with the back of the screwdriver, flex the board, press each corner of each large chip, especially BGAs.
Use a can of compressed air turned upside down and spray shortly on chips and see if it does something.
Check shorts between ground and power pins.
Next, for component checking: check diodes and caps for shorts, check [SMT] fuses for open. Check transistors and other 3 pin devices for shorts.
Check ground continuity, though it's not usually a problem with production boards.
Power up the board and check for voltages, especially on the controlling part, if there is any. I.e. the part that should have a standby voltage like buttons, LCD, I/O. Check for voltage correctness, 0.2V lower than design could mean non-functioning board.
Buy a new board.
If acquiring a new board is out of reach, try to read socketed devices with a universal programmer. Try to use JTAG or other protocols on the board.
Start replacing chips on the old board. Start with the cheap and accessible ones (power regulators, opamps and comparators, dil, tssop and sot-23 packages) and work your way up to BGAs.
Unless it's really specialized equipment no one working for money would try the last step.