JOEL - Many have a hard time knowing for sure when they have received answers to prayers. A lot of it has to do with how we pray and how we ask things of God. Sometimes we go to the Lord with a problem and just flat out ask Him what to do. We expect to see a vision or hear a voice telling us exactly what to do. This almost never happens. God usually expects us to figure it out on our own first, make a decision and then ask Him if it is right.
Oliver Cowdery received a special revelation from the Lord teaching him that principle:

"Behold, you have not understood, You have supposed that I would give it unto you, when you took no thought save it was to ask me." (D&C 9:7.)

If our decision is correct, we can have a peaceful warm feeling inside; the Holy Ghost confirming that we have made the right choice. If not, we have a stupor of thought; uncertain of what the answer is.
Much of this depends on the intent of our heart. We are much more inclined to get an answer if we are asking for a righteous thing and if we have strived to keep ourselves in tune with God and His spirit.
Pres. Marion G. Romney said,

"When confronted with a problem I prayerfully weigh in my mind solutions and come to a conclusion as to which is best. Then in prayer, I submit to the Lord my problem, tell him that I desire to make the right choice. Then I ask him if I have made the right decision to give me that burning feeling within. When enlightenment and peace come into my mind, I know the Lord is saying, yes. If I have a "stupor of thought" I know he is saying ,no, and I try again, following the same procedure."

If we don't seem to get any answer it could be that the problem we are praying about really isn't as big or important as we think it is. Many times it doesn't matter which way we choose(eg. which house to buy, which school we go to, etc.). If we are trying to live right, the Lord will bless us no matter what we choose to do.
President Brigham Young said,

"If I ask the Lord to give me wisdom concerning any requirement in life, and I get no answer from him, and then do the very best that my judgement will teach me, he is bound to own and honor that transaction, and give the divine help that I need."

Sometimes we ask with impatience, expecting to get an immediate answer. Sometimes when the Lord doesn’t answer our questions immediately, or within a day, or a week, or a month we tend to think He will never answer. We must be patient and be ready for the answer when it comes.
Sometimes when we pray we aren't really listening for an answer nor do we wait for the answer. After praying we immediately jump up and leave not giving time for the spirit to influence our minds. Or there may be other distractions around us that keep us from being focused enough on what we are praying about. These things can prevent us from getting the promptings we need.
We also must remember that the "burning in the bosom" is not the method of answering prayers that the Lord mentions the most. In revelations to Joseph Smith, Oliver Cowdery, and Hyrum Smith, the Lord talks about answering prayers by enlightening the mind, speaking peace to the mind, telling the person "in your mind and in your heart," filling the soul with joy (see D&C 6:15, 23; D&C 8:2; D&C 11:13-14). He will speak to us in ways that will be most effective for our own conditions. We must learn to recognize how we feel when the Spirit is with us and when he is communicating to us. It might be different for different people.
Most of all don't give up on God. He does care about you and loves you and wants you to succeed.