just to state the obvious, is there a setting on the TV as to where it gets its source from, like, AV1, AV2, HDMI1, HDMI2 - that sort of thing, and you have changed that setting to match the HDMI port you are using?
what's the age of the TV and PC?
what HDMI versions do they support; HDMI 1.2, or 1.3, or 1.4 etc?
same for the cable, some cables are built for certain HDMI versions.