How much Carbon Dioxide would be required to displace enough oxygen to prevent ignition?
The parameter you are asking about is called the Minimum Oxygen Concentration (MOC), and is a measurement of the minimum amount of oxygen present in air to propagate a flame. The amount depends on the fuel being burned, and varies from about 4% for hydrogen to about 18% for some solid combustibles.

Let us consider your example of butane, and round some numbers to make our calculations simple. Butane has a MOC of 12%. Normal oxygen content in air is 20%, with nitrogen and sundries making up the remaining 80%. Assume uniform mixing and displacement of gases is equal. In order to reduce the oxygen content to 12%, you need to introduce enough CO2 to make up 40% of the air content:

$O2 + N2 = 100$  =>20 + 80 = 100%

$O2 + N2 + CO2 = 100$    => 12 + (12*80/20) + CO2 =100%

However, let us consider a couple of other very significant points. 


An oxygen level of 12% is unsafe. Anything below 19.5% is unsafe. At levels of 12%, a person will have impaired judgement and coordination, and experience increased pulse rates. Prolonged exposure can have fatal consequences.
A CO2 level of 40% is fatal. Full stop. Levels above 7% can cause loss of consciousness and just 10% can be fatal.
CO2 is actually denser than air, so mixing of the main components is unlikely to be uniform. This means that higher CO2 concentrations will be found lower down in the room.


I hope you stay well clear of your basement until you have resolved this problem and have appropriate active ventilation installed, as well as possibly an oxygen monitor. 

In the very least, get yourself a canary.