Problem Flashing ESP8266-01
The blue LED is connected to the TXD line of the esp-01, it flashes when something is sent on the serial port.
The shipped firmware that responded to AT commands is overwritten when you flash something else onto the chip, like another firmware or random garbage.
If you are reading 

    ets Jan 8 2013,rst cause:2, boot mode:(1,7)


Then the serial port baudrate is correct. 
It seems to me that all you require is some valid firmware or a copy of the firmware/program you deleted to begin with.

    esptool.py --baud 115200 --port /dev/tty.usbserial-A50285BI read_flash 0x0 1048576 backup.bin


will copy the contents of a new esp-01 to your hdd so you can write it back when your own program fails. That way you can still use the AT commands.