Starting my Fujitsu Lifebook E754 only the NumLock LED flashes,

That would suggest the basic power supply is running (LED lit) but that the motherboard has a problem (BIOS won't start).

Do you have the right keycode to enter BIOS?  

How old is the machine? Any warranty?  

Otherwise it may be time to replace.

remove and reseat the RAM SODIMMs

@Author,

This sounds like a mainboard/Motherboard issue as @john Stated above. This is backed up by the following article :

reference : https://forum.ts.fujitsu.com/forum/viewtopic.php?t=47317

Actually it could be starting up, but your laptop screen may be dead.  Try plugging in an external monitor. Then restart (power off then on).

the only thing you can do is remove/disconnect all external and internal devices : disk, cd rom etc - hust leave mobo - cpu and ram
then check if you can enter the bios with Del or f2 key

Experts, on this style notebook, the number lock key works almost the same as the BIOS beep codes. From what I have been able to see, there is a troubleshooting code register that goes along with the button light flashes.

Laptop LED Blink on Startup There are many reasons that a computer does not...
Laptop LED Blink on Startup
There are many reasons that a computer does not startup or boot into the Windows operating system. If your computer will not start or boot, you will see or hear symptom to indicate the general area of the problem.
Startup Symptom: LEDs blink but does not start
The blinking LED lights on newer computers, or the beep tones on older computers, will help support agent determine what hardware component is not responding properly. The exact meaning of each code varies with the model, and the user cannot change any of the blink or beep codes.
DO THESE FIRST - Perform a hard reset.
If a PC suddenly fails to boot properly, you should perform a hard reset as the first procedure.
1. Disconnect all peripheral devices and remove all USB devices and media cards. You want to test the computer not the accessories!
2. Disconnect the AC power adapter, remove the battery and then press and hold the power button for at least 15 seconds.
3. Reconnect the AC power adapter (but do not connect the battery), Press the Power button, Look for glowing LEDs near caps lock and num lock keys, and Listen for sounds of a disk drive and fan turning.
Identify the number of blinks or beeps
When there is a start-up problem and you see LED lights on the keyboard blink a few times (between 1 and 8 blinks) do the following actions.
Table of Sample Blink Codes
The following table illustrates the meaning of blink codes used on some notebooks. The blink or beep codes on your computer may have different meanings.
Meaning of Sample Blink Codes for some EFI Notebooks:
1) Number of Blink: Continuous Glow, Blinking LED: Battery power LED, Component: Battery,
Error Condition: The AC adapter is attached and the battery is charging, but does not yet have sufficient charge to power the notebook.
2) Number of Blink: 1, Blinking LED: Caps Lock/Num Lock, Component: CPU,
Error Condition: CPU not functional
3) Number of Blink: 2, Blinking LED: Caps Lock/Num Lock, Component: BIOS,
Error Condition: BIOS corruption failure
4) Number of Blink: 3, Blinking LED: Caps Lock/Num Lock, Component: Memory,
Error Condition: Module error not functional
5) Number of Blink: 4, Blinking LED: Caps Lock/Num Lock, Component: Graphics,
Error Condition: Graphics controller not functional.
6) Number of Blink: 5, Blinking LED: Caps Lock/Num Lock, Component: system board,
Error Condition: General system board failure.
7) Number of Blink: 6, Blinking LED: Caps Lock/Num Lock, Component: BIOS,
Error Condition: BIOS authentication failure.
8) Number of Blink: Continuous blink, Blinking LED: AC power adapter LED, Component: Power adapter,
Error Condition: Insufficient power
Common solutions for issues that cause blinking LEDs or beep tones
When the computer can boot into the BIOS, run the memory test to identify other issues.
Check for loose connections and test the memory
Blink codes are often displayed after a user adds memory to the computer but does not seat the module properly. The LEDs may also blink error codes if a hardware component is loose because the computer was dropped or jarred. The problem could be that the stick of memory or one of the memory slots has a bad connection.
Check for loose memory modules
If a memory module is loose or is not making good contact with the memory slots, the computer does not recognize all of the memory. Reseating the memory module may resolve memory failure errors.
on Mar 21, 2011 | Computers & Internet

site reference : http://www.fixya.com/support/t20513670-fujitsu_s6520_when_start_num_caps