you're going to need to know at what voltage the computer will turn itself off at. Then maybe doing it like a RC time constant problem.
Let's say it shuts off at 80% of full voltage, because it's drawing 3.5 amps (I just used what you supplied) 19/3.5 = 5.43 which we will use for R.
T=RC= amount of time it takes for voltage at the cap to decay to 63%.
so work it kind of like an exponential decay and you have your answer.
About 1.2 seconds at that current.
I cheated and used this
calculator though. I'm pretty sure the percent is not a percent
of voltage it's percent
from voltage. So I used 20% for the example.