It's hard to see the full picture of what's going on with the little piece you provided - it could just be a timing issue. It sounds like your BF frequently gets on the computer and it was during this time you asked him to chat. Maybe this was his "relaxation" or "down" time and he felt you were robbing him of that. Would he be open to chatting while he was at the computer - if you just need someone to talk to and not really care if they're listening, maybe that could be an option. Or find a time to ask him to chat when he's not on the computer. Or work out a compromise sometime when he has your full attention (which sounds like avoiding times when he's on the computer).
I don't see anything wrong with wanting to chat, however, sometimes if a guy is in a habit and you catch him off guard with a request like this, you may not get the reaction you were hoping for. Just something to be aware of and not take too personally at first. Could just be another compromise to work out.
If after you have a time to discuss this, and he's still not responsive - then you may want to consider if he's really the one for you to stick with...
Good luck.