Stopping PC from building up static

A PC that is properly grounded will not build up static. Check your wall outlet for proper grounding. If it isn't, repair it (or have it repaired). You NEVER want to attach a "live" wire to exposed surfaces.

If your computer is plugged into the wall (grounded) then it shouldn't build up any static. It's likely that you are the one carrying unbalanced charges, and discharging through your computer. You may also just have a faulty keyboard.

holy crap... something is very wrong. computer cases are made to be grounded... it's a phenomenon known as a Faraday cage. Your case should not be building up static electricity... something is shorting or grounding out wrong inside the case. and might fry your system if you don't hunt it down.

While it is true that computer cases are made to be already grounded, there are a few things that can cause an issue.

Does the electrical outlet have proper ground? Many older homes do not have a proper ground. You may need an electrician to help you to determine this one, but would be cheaper than buying a new computer after this one fries.

Is the case sitting on the floor? Is the floor carpet or plastic linoleum?

If so, remove the computer temporarily from the area, and spray the floor and wall behind it with a product called "Static Guard" or something else like it. It would be best to set up a small wood riser shelf for the computer to sit on and keep it off the floor.

Your computer should never sit on the floor!

It could also be that the cables laying across the floor are picking up and transferring the static. Use twist ties or whatever to get those cables organized and off the floor.

If your keyboard cable is laying across the carpet before it reaches your desk (rare, but happens in some setups) then that is also a bad "no no." Get it off the floor.

Static can do more than cause issues with a keyboard or other peripherals, it can fry your entire computer if enough builds up. Get it taken care of quickly.

I do not suggest attaching a wire as you mentioned. As the static can be passed from the flooring, through the radiator, to the computer, it will only add a point of entry for the static, depending on the surrounding setup. It is best to separate the computer from the source of the static to begin with.

Now, all that being said, and since I have limited information on your layout/setup, and since I want to be thorough in trying to help, then let me add another possible source. You stated it is your keyboard having the issues. It is possible that the static is coming from your fingers into the keyboard, which means you are building up static walking across a carpet to the computer, then sitting down and zapping it. You can place a small metal plate at your desk with a wire running to said radiator, and touch it to "discharge" your static buildup before you touch your computer. If the source of the static is you, then this may help.