Philippians 4:6 tells us
"Be anxious for nothing, but in everything, by prayer and supplication with thanksgiving, let your requests be made known unto God."
In Acts 1:13-14, after Jesus ascends, we see
"And when they (the Apostles) had entered, they went up to the upper room, where they were staying, Peter and John and James and Andrew, Philip and Thomas, Bartholomew and Matthew, James the son of Alphaeus and Simon the Zealot and Judas the son of James. All these with one accord were devoting themselves to prayer, together with the women and Mary the mother of Jesus, and his brothers."
Acts 2:42, Acts 3:1, Acts 6:4 and Acts 12:5 all mirror this - the need and dependency on prayer.
So, why do we pray?
For a number of reasons. We pray because it is a form of serving the Lord (Luke 2:36-38). We pray in preparation for major decisions (Luke 6:12-13); to overcome demonic barriers (Matthew 17:14-21); to gather workers for the spiritual harvest (Luke 10:2); to gain strength to overcome temptation (Matthew 26:41); and to obtain the means of strengthening others spiritually (Ephesians 6:18-19).
Does God know your father is in the hospital in need of help?
Absolutely. His eyes are everywhere (Proverbs 15:3), and He knows all things (1 John 3:19-20).
Do your prayers prompt God to action?
Yes and no. God is no respecter of persons (Acts 10:34), and all things are in accordance to His will and if you ask as such, He will hear you (1 John 5:14). By praying to the Lord, you are showing Him you need Him. A perfect analogy would be like this - are you yourself more likely to help someone asking in the heat of the moment, or someone asking out of true sincerity?
If you don't prompt God for action, will he help your dad anyway?
Absolutely. God does not need to wait for you, or anyone else, to take action. He is above all things, and everything moves in accordance to His will. He does not want you or your father to suffer, and the odds are with you that He will help you and your family through this tough time.