Let's start with a stationary Earth. If we smash a few Mercury-sized objects into the Earth, the Earth begins to accrete mass. Repeat this step with larger and larger objects, until we start impacting Jupiters into the growing Earth. If we cause an even larger planet to crash into the Earth (say, a 3-Jupiter mass object), we will eventually reach the boundary between planets and brown dwarfs. If we continue accreting more Jupiter-sized objects to the Earth, we will pass the brown-dwarf limit of 90 Jupiter masses, we will reach stellar masses. But instead of turning into a star, this object either stays molten as a "planet", blows itself apart, or even collapses into a black hole. I tested this in Universe Sandbox 2 about 20 times, and none of them coalesced into a star. Why does this happen, and would this be realistic?
Who can say for sure? I guess the physics in Universe Sandbox is not good enough.
What I would say though is that if you have a "protostar" that contains a higher proportion of heavy elements than a usual star, then the threshold for ignition of hydrogen will be lower than 75 Jupiter masses (e.g. How large can a ball of water be without fusion starting? ). If on the other hand it contains very little hydrogen (not enough to sustain a significant main sequence reaction rate), then it will be forced to rely on He, C or even O burning that require significantly higher temperatures and a much more massive object - probably in the region of 1000 Jupiter masses.
However, if you are telling us that some of your simulations collapse into a black hole at 90 Jupiter masses, that suggests that a more simple explanation is that the simulation physics is incorrect. I also think it would take a very peculiar composition indeed to avoid a nuclear burning phase prior to collapse to a black hole, even if you give the object several stellar masses of material.
To create a star you need hydrogen and helium. Therefore, you need a gas giant, not a terrestrial planet, to let it turn into a brown dwarf, and eventually into a hydrogen-burning star. You write of accretion of Jupiter-sized objects, but are these gas giants? Universe Sandbox features some exoplanets whose composition is unknown well.
When I make Jupiter have 80 times its mass in Universe Sandbox, it turns into a red dwarf star. When I make it have ~50 Jovian masses, it starts to emit own light already. However, it's very difficult to add mass by colliding bodies with each other in Universe Sandbox, as this makes them lose mass rather than gain any. I did this the other way round: After a collision with Proxima Centauri, guess what? Proxima lost so much mass that it eventually had about Saturn's mass, no more emitted own light and looked like an ordinary gas giant.