I think all Christians have gone through what you've just described, so you're not alone, friend. I suppose the first question I'd ask yourself is: What was the motivation to pray and to go to church? If you pray and attend worship out of a sense of duty or to get something, then it is inevitable that your spiritual life will continue to be dry, boring and exhausting. Listen to what Pastor Tim Keller says:
There can be long lists of things that we pray for, and long lists of Bible verses we read, and long lists of things we thank him for. Yet there is no fire. Why? If we lose focus on the glory of God in the gospel as the solution to all our problems, then we devolve into a set of "grocery list" prayers, made rather desperately. When we are done, we only feel more anxious than before. The presence of God is not sensed because God is really just being used – he is not being worshipped.
Instead, we should always remember that the first thing we need is a new perspective on our needs and problems. We should always intertwine with repentance over our unbelief and indifference to God's grace. On the one hand, we must "pray into" ourselves that the thing we are asking for is not our Savior or God or glory! But, (on the other hand) after we repent and refine our desire, we should "pray into" ourselves that God is our Father and wants to give us good things, so we can ask in confidence. Also, intertwined with our petitions should be praise and marveling that we are able to approach God, and be welcomed in Christ.
This is gospel-centered prayer, rather than anxious petitioning. Our desires are always idolatrous to some degree, and when we pray without dealing with that first, we find our prayers only make us more anxious. Instead, we should always say, in effect, "Lord, let me see your glory as I haven't before, let me be so ravished with your grace that worry and self-pity and anger and indifference melt away!" Then, when we turn to ask God for admission to grad school or healing of an illness, those issues will be put in proper perspective. We will say, "Lord, I ask for this because I think it will glorify you – so help me get it, or support me without it." If the overall focus of the prayer is on God's glory and the gospel, our individual petitions will be made with great peace and confidence.
So friend, the first thing I'd do is to examine your motives and start praying for God to reveal his presence to you. Don't immediately pray about what you want; pray for God's presence to fill your life. That will ignite your passion again and again!
Second, on a more practical note, are you getting enough rest? If you are exhausted and leave your prayer (& devotion time) at the end of the day, you can't devote your best energy. I would suggest you try another time to pray. Usually, I spend some time in the morning to do my devotions as I have the most energy and alertness. In the evening, I only say a short, 'goodnight' prayer to God. For additional information, I recommend you read this blog post about "devotional times."
[Answered by Pastor HM]