I think Branwell's death cert said bronchitis and possibly 'marasmus' (which is now only used, I think, to indicate malnutrition in children), but it's hard to rule out anything in a self-neglecting alcoholic and drug addict!
Don't forget the other two Brontes, the eldest two, Maria and Elizabeth, who died in childhood after their stints at Cowan Bridge School, Maria (on whom Helen Burns in Jane Eyre is based, as Cowan Bridge became Lowood) of typhoid and Elizabeth only a few weeks later of TB. Ironically, if they hadn't become ill and died when they did, it's very possible Charlotte and Emily, who were also at the school would have died too - it was only the ill health of the older ones that alerted Patrick to how appalling the school regime was.
I think part of the reason their deaths seem so appalling to us - even given that all the Brontes but Maria and Elizabeth lived longer than the average lifespan in Haworth at the time, which was 19! - was how domestic and unmediated they were. Emily refused to see a doctor when it was obvious she was dying, refused to even have her health mentioned or take medicine, and until the day of her actual death, she got up and did her housework as usual. She only said she would see a doctor within an hour of dying, when it was useless, and then just died on the sofa in the parlour.
And five months later Anne was fulfilling a last wish to see the sea in Scarborough with Charlotte and their friend Ellen Nussey, and as they were actually closing her eyes in their boarding house room, a servant stuck her head around the door to announce dinner. You'd need a heart of stone not to weep for poor Charlotte, losing three siblings in a year.