Problem flashing esp8266
I've had the same problem and seems that I resolved it. Different ESPs have different memory addresses for the firmware. The AT firmware consists of more parts, as you already mentioned. Mine were these, finally the correct values (bins taken from ESP8266-firmware-at-github):

boot 00000
user 01000
blank FB000
init_data_default FC000
blank 7E000
blank FE000


How to troubleshoot:

1, check if the ESP is booting. Set baud rate at 74880 and reset the ESP. This is the baud rate at which the boot sequence can be observed. SHuold look like this:

ets Jan 8 2013,rst cause:2, boot mode:(3,6)

load 0x40100000, len 612, room 16 
tail 4
chksum 0x12
load 0x3ffe8000, len 788, room 4 
tail 0
chksum 0x50
load 0x3ffe8314, len 264, room 8 
tail 0
chksum 0x4a
csum 0x4a

2nd boot version : 1.1
 SPI Speed : 40MHz
 SPI Mode : QIO
 SPI Flash Size : 8Mbit
jump to run user1


⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮⸮


2, Is the user program portion running?

jump to run user1


This is the part where it says how the code is being run and if it errors out. 
If you get something similar to this, that's definitely wrong and you have flashed the wrong bin to a wrong memory address and / or used an incompatible firmware:

...
SPI Speed : 40MHz
SPI Mode : QIO
SPI Flash Size : 8Mbit
jump to run usererror user bin flag, flag = 6


3, Check out my struggle -> ESP-01s 8266 brick and revive - hope it helps, there are some more details, including a schematic etc. I have chosen to go the Linux / Python way, but the approach is more or less generic, I think.