How long have you been praying over your current request? I am recalling the time I prayed for four years--and yes I, too, felt ignored and neglected after only a week. I can be stubborn so I kept on. And then one day...it all came together...and my prayer was answered in a way I did not expect. It was then I realized God had been working with me all along. There had been amazing coincidences that at the time I did not recognize had anything to do with my prayer request.
I learned that God's work does not happen in the time it takes for us to snap our fingers. He is a true artist who takes time and effort over every single detail.
The type of prayer that works best for me during the lonely times is contemplation. Contemplation is totally quieting the mind, thinking of nothing at all (as best that can be done) so that God has time to work in the peace and quiet. Sometimes you may be surprised how it refreshes you as well.
Keep the trust that God cares and loves even during the dry, dark times. I wish you peace, I wish you well.