As patio said, a good reseating sounds like it's in order (that is, remove the video card from its connecting slot on the motherboard [WARNING: be sure power is disconnected and flushed. Remove the power cable from the power supply, then press and hold the power button until the LED indicators and/or fans cease activity], clean the connector and connecting slot, and reinstall the card).
Whenever working on internals/electronics with open circuits, it is wise to use ESD personal protective equipment (such as an ESD wrist band) to avoid compromising electrical components via electrostatic discharge (ESD). ESD occurs when a difference in voltage between two bodies is sufficient enough for electrical current to flow (and in most cases, peripherals like RAM and graphics cards can be damaged by ESD without even feeling the discharge/"static-shock").
When removing the graphics card, be sure to mind any retaining clips that may need attention before pulling the card out. Once out- Inspect the contacts on the graphics card and gently remove any dust with a can of compressed air. Re-install the graphics card into its slot- make sure to re-attach any connectors that came off such as PCI-e power connectors. Re-assemble the case and plug the power cord back in.
if this does not work, try connecting to your monitor using a different port (if using HDMI, try DVI(usually a white connector) if available. Or if using DVI, try D-SUB/VGA connector(usually blue) if available. Sometimes ports go out too, as happened to me a few years back (this is pretty rare though).
