Connect PC chassis to the ground of TV coax cable?
Static discharge to ground suggests that your house wiring ground circuit is ineffective (floating). Very old house power distribution was 2-wire.
Every PC has a three-wire power plug that expects to see a safe path to earth on its ground pin to protect you and internal static-sensitive electronics.
However, I would be reluctant to invite lightning into my home by a cobbled-up connection to ground. The term "ground" may ease your mind, but lightning has a way of not respecting the path you have provided for it.
The interconnection of devices to a PC is often complex, involving multiple devices, each of which is powered from the same AC source (monitor, amplified speakers, modem etc). I would plug all these devices into one power bar, and attach your grounding connection to that power bar only. Nevertheless, don't expect this grounding method to save your equipment from even nearby lightning strikes. Re-wiring your house might be a safer option - would it pass a fire-safety inspection?