Modern computer equipment is remarkably reliable. When things do go wrong, they can often be solved by very simple procedures.
Before calling out the service engineers, take the trouble to run through the procedures shown here. They may just save you both expense and embarrasment.
Check the obvious first:
Power cable firmly attached to the computer and to the mains socket?
Mains socket switched on?
Power available at the mains socket? Try plugging something else into the socket and confirming that works.
Then check the less obvious:
Fuse not blown in mains plug?
Is the computer itself working but not the display? Listen for the sound of the computer's fan, check for power light.
Power getting to the display? Run the checks shown for the main computer, above, for the display.
Display lead firmly attached at both ends?
Video display card firmly seated in its socket?
Wherever components attach to one another, the commonest source of trouble is the connection(s) between them, so check the following:
Is the component seated correctly?
If attached by a cable, is the cable seated correctly at both ends?
If the component includes jumpers or switches, are these set correctly for the installation?
If this is a new connection, or a reconnection, has a pin got bent or broken? Check plugs with a magnifying glass.