What is a word that describes a person who has difficulty speaking with girls?

"Shy" would be a description of someone who has difficulty speaking with people. You could describe someone as "Shy around girls", but knowing more about why they were shy might lead us to a better phrase.

I've seen in various old books (Vanity Fair, if I rightly recall) such a person described as a hobbledehoy, meaning an awkward, tongue-tied young man.

parthenophobe

In psychology, Parthenophobia refers to an abnormal and persistent fear of virgins or young girls.

^{Psychology Wiki}

Someone who has difficulty speaking in stressful situations (such as the computer programmer and the girl) may be described as "tongue-tied".