|Since you get an onscreen message saying there is no signal there is nothing wrong with the monitor. You have tried a different "vidoe and card" ( presume this means a different monitor and swapped out for a known good graphics card) then your statement "the computer runs right" is clearly mistaken.|
The computer is not running right.
As to the possible reasons, there are many beginning with the powersupply. It is possible for a powersupply to partially fail allowing things like fans to spin up and CD drive trays to open/close, yet not provide sufficient power to other motherboard components. Do you have a spare compatible powersupply of equal or greater capacity?
Does the system give any BIOS beeps when you try to start up?
Does the motherboard have an inbuilt graphics adapter or only the plug-in card?
What make/model motherboard? Is it a brand-name OEM system or was it custom-built? What CPU does it have? What brand and specification powersupply does it have?
It is possible any of the other components may have failed including CPU,Motherboard, RAM, Drives, PCI Cards, Even something as simple as a failed CPU fan will prevent many systems booting.
Goin' Fishin' (Some day)