What to do if the father of my child has been ignoring my requests to talk about what he wants his involvement to be with our soon to be born child?

You actually have a couple of different issues-- so I'm going to break them up to make sure that everything is covered:

The first is about communication with your ex-.  Having a child is one of the most beautiful experiences that any person (man or woman) can go through.  Despite the miracle of birth, the law does not require the father of a child to show any interest in the pregnancy.  His duties don't kick in until the child is actually born.  So, if he has been ignoring your requests to be involved, you need to simply make a decision on whether you even want to have him involved.  Forcing communication often backfires and only creates more hard feelings.  If you feel it's worth the effort because there have been signs that he is interested, then, by all means, continue the effort to communicate.  Otherwise, chalk-up his lack of communication with you as a loss to him.  Your focus really needs to be on a healthy child--not a self-absorbed jerk.

Your second question is regarding custody.  The courts will use a standard called the "best interest of the child."  If the court finds that allowing him unfettered access to the child is in the child's best interest-- then they will grant him 50% custody.  However, you actually have a couple of good factors working in your favor that suggests that would not happen.  Your first major factor is his lack of involvment in the pregnancy.... if he continues that trend, you're not likely to see much of him after the birth of the child.  If he shows little interest in the birth of the child--- and then shows little or no interest in the child after it's born, the courts are not going to grant him equal custody six months or more down the road.  Parenting is full-time--- not just when they decide to get involved.  Your second major factor is that this is an infant.  Even though courts are not allowed to use gender as a basis for deciding custody, many still use it as a "consideration" when the case involves an infant.  There is a concern of the child being with the mother as such an early age.  Your third factor is related to the his lack of involvement -- but is more financial.  If he does decide to file a custody suit and he really wants a battle, ask the court to require him to reimburse you for one-half of the medical expenses that you incurred as a result of the pregnancy.  This extra expense will either deter his filing or will scoop-up some of the funds that he would have used to give his lawyer to fight for him.  (Few family lawyers do extra fighting for free.)

Other factors can influence a court's decision and you can start working on those factors now.  The court will want to make sure the child has a safe, happy, and adequate living space.  This means a crib/bed, a highchair, and all of the usual baby equipment.  Pictures of a fun nursery are great evidence for the judge to look at.  Research things that you can and will do with your child.  For example, if there is a zoo or learning center nearby, scope those out as potential developmental activities.  If you are a working mom, make sure that you research child care options now.  Essentially, what you want to show the court is that you are serious about parent-hood.  When the court turns and asks him what kind of car seat he has, your ex- is likely to say "he's working on it."  A judge will be less than happy with an absentee dad, demanding custody, who has done absolutely nothing to prepare for parenthood. 

There are also some things that you should not do.  Ex's are always frustrating-- and being pregnant doesn't make it any easier.  It also sounds like he's trashing your name a bit with this whole "it's probably not mine" line.  With that, many new moms tend to let the pressure get to them and they make less than stellar choices while under this stress.  Don't get in shouting matches, fights, or resort to any non-approved medications because you lost it or you don't know how to control the stress.  Instead, invest in extra bubble bath or chocolate-- deal with the stress-- and don't let him goad you into a stupid mistake that will come back and haunt you in a custody battle.  You are in a good position right now for retaining custody.  If you test positive for a controlled substance right after you give birth (because you couldn't handle the stress), then more than likely, someone will be picking up your child and delivering it to him.  If you say or do something stupid or threatening, you'll be hearing it later in a custody hearing. 

Bottom line, be a good mom during and after the pregnancy-- and you shouldn't have any problems with a custody battle.  You've been given a gift-- enjoy it... and the rest will workout.