|There's nothing wrong with the monitor so taking it in together with the system case would not have made any difference.|
The problem is either inside the system case, or the signal cable may be faulty so try a new cable.
Another possibilty is if the PC has an integrated graphics adapter plus an add-on graphics card. That means there will be two VGA ports at the back, but only the add-on one will actually work, so make sure the monitor cable is connected to the correct one.
It's also possible that whoever worked on your PC may have dislodged the graphics card, so check that it's firmly seated inthe slot (remove it and put it back, this will clean the contacts).