It could be one of several different issues that you'll need to troubleshoot to find out what could possibly be causing it not to boot. You may have a corrupted RAM stick which might cause it not to boot up, you can try removing one of the ram sticks and turn on the computer with just one ram installed.
Also sometimes there is a pattern to the blinking light that you see and if you look up the specific blink code for that model it will tell you what the problem. Have a look at this service manual, it has the error blink codes and what you could do to solve the problem.
[http://ftp://ftp.dell.com/Manuals/all-products/esuprt_laptop/esuprt_latitude_laptop/latitude-e5400_Service%20Manual_en-us.pdf]