Although density altitude does reduce performance of an aircraft, it doesn't automatically keep you on the ground.

Is there a plug and chug way to do it if I know my barometric pressure, temp, and altitude? I need to get it everyday before I have a flying lesson. I hate using that round slide-rule flight ...

Adding the two issues together means a high-altitude airport on a hot day has less dense air at lower pressure. Pilots calculate this to determine the density altitude.