if medulla is damaged :
The medulla contains the cardiac, respiratory, vomiting and vasomotor centers and deals with autonomic functions, such as breathing, heart rate and blood pressure. It is located at the base of the brain stem.
If damaged it can change your breathing rate and/or heart rate. Our bodies need to have these functions with in a cretin range in order to function properly. It they are too slow or fast, it could make us sick or even die.
if pons is damaged:
Damage to the pons will result in a range of effects on sleep. For example, damage to certain parts of the pons can put a person into a semi-permanent sleep-like state. Research with animals has also shown that damage to the pons can cause an animal to sleep much less than prior to the damage.