I haven't gone through this personally but I've known someone who has, and was well counselled beforehand about contacting the parent found and what to expect. It doesn't sound like the company you used did any proper preparation with you.
It is quite common for the parent not to want any involvement, particularly if they were already aware of your existence and chose not to be in contact before (there are other circumstances, such as when the father is unaware that there ever was a child, or the other parent has removed the child and disappeared and the remaining parent is unable to find them). You really should have been prepared before sending the email, did you receive any advice at all?
I would advise you not to phone as it forces an immediate response. If you are worried that the email hasn't got through, send a letter. And make sure you get proper support. For example, it is relatively normal to receive a reply several months later, don't expect an immediate reply; if he does want any contact, it may take him a long time to process the information and decide what to say.
Before you write, research carefully what you are going to say. Do you want medical information from him to help with potential genetic conditions? Are you able to reassure him that the past is over and you won't be asking questions about why he abandoned you, or do you actually want to talk about these things? Are you looking for closure, for an ongoing relationship of some kind, for information ...? Be clear in your own mind about what it is you want to achieve by making contact.