What you are all saying is correct and in an ideal world it would be wonderful if it was actually that simple.
From my perspecitve, the suggestions given so far will not give much benefit to the OP or are necessarily the best ways he should go about it, simply because the OP will not get anything done in a timely fashion that will also benefit his business.
Clearly, the seller has (possibly an unknown) has put complete control of the situation into the hands of the prospect, straight of the bat, you unfortunately deminish your percieved value and someone they should not be doing business with. Your not worth it and easily forgotten. buyers only close business they do not want.
There is a fine line between appreciating that the potential client is busy, and being persistant without coming across as needy or desperate. What you, as clients say you prefer or rather what is being stated above as to what is prefered, is not what you will really respond to.
I say this from working in an international sales role, althought the approach may differ from culture to culture, between cold or warm prospect, an American will respond to the same things as someone from Zimbabwe. We are all human with predictable behaviours, after enough calls, past conversations become a blur and former patterns of interaction start to emerge.
so this is what you do:
You pick up the phone and call the prospect.
They will be busy or in a meeting (they did answer the phone), or palm you off with some viable objection. No worries, sell your sales call before you start selling, get an appointment, and go from there, follow up with an email confirming the apointment. then follow through with your pre planned sales script.
if they give you S%^t or in anyway make you feel less important than them, give it back, dont be afraid to p!$$ them off, or tell them they are not as busy as you, dont be afraid to lose them. if they get angry or you get any form of emotional reaction from them, this is great, they will likely stay on the phone to argue and debate. You have bought yourself more time and you now have a relationship, albeit a negative one. This is prefered than being nice and palmed off. Now from here, you better have something of value to say and turn it around, the swing in emotions will make you golden, then you will be in.
when you start selling, you focus first on attraction/creating spark for your proposed plan or solution to their need. Get them excited on their fears and greed by asking disturbing questions or ones of elations for what your product / service could actually do for them.
they will start to open up and give you signs of interest, they will talk more, ask questions, maybe donate more information than was actually required.
This is where you move to making them conformable, dont start by trying to gain rapport, this is a trap.
then close, ask for the business if you have to.
Do what gets the job done.