I can think of a couple of things to try.
First, hold the power button down for at least 10 seconds. This is supposed to force a reset of the system. If that doesn't work, you may need to get it serviced again. I'd take it back to whomever did the repair and have them check it over.
The other thing to check, and this is unlikely because it sounds like your system isn't booting because the fan is coming on at full speed, is to use a bright flashlight on the screen to see if there is any image there. Sometimes, the backlight setting gets turned down all the way for unknown reasons. The keyboard keys should adjust it, but may not. In this case you would need to attach an external display and adjust it that way.
An external display is another option to determine if the system is booting or not.
Good luck!