Its a SMD board, its dead/damaged, throw it out (unless you have the skills to do smd rework)
Its most likely either a dead mega chip or dead stepper drivers... which, does it mater?, you can't fix either.
as a Final test, download the ramps test program [reprap.org]
update the pins for x y and e for those on e0, e1 e2 on rumba
#define E0_STEP_PIN 23
#define E0_DIR_PIN 22
#define E0_ENABLE_PIN 24
#define E1_STEP_PIN 26
#define E1_DIR_PIN 25
#define E1_ENABLE_PIN 27
#define E2_STEP_PIN 29
#define E2_DIR_PIN 28
#define E2_ENABLE_PIN 39
run the test, if e0, e1 and e2 aren't all moving.. its dead. Get yourself a new board, put it aside to practice hot air rework on.
Its most likely either a dead mega chip or dead stepper drivers... which, does it mater?, you can't fix either.
as a Final test, download the ramps test program [reprap.org]
update the pins for x y and e for those on e0, e1 e2 on rumba
#define E0_STEP_PIN 23
#define E0_DIR_PIN 22
#define E0_ENABLE_PIN 24
#define E1_STEP_PIN 26
#define E1_DIR_PIN 25
#define E1_ENABLE_PIN 27
#define E2_STEP_PIN 29
#define E2_DIR_PIN 28
#define E2_ENABLE_PIN 39
run the test, if e0, e1 and e2 aren't all moving.. its dead. Get yourself a new board, put it aside to practice hot air rework on.