df <- data.frame(t1 = c(10, 20, 30, 1, 0), t2 = c(30, 0, 40, 0, 0), t3 = c(10, 0, 3, 10, 0))

df<- df%>% rowwise() %>%
  do({
    th <- c(.$t1, .$t2, .$t3,)


    data.frame(., t_s_last = min(th[th > 0))
  })

apply(df, 1, function(x) if(all(x==0)) 0 else min(x[x> 0]))