Hi Morph
To echo everyone else - Welcome to the site bro, it's great to have you here.
Wow so new job, new baby, only been married 3 years ... that’s a headfull. 😉   
Mate couple of things I could say but sounds to me that the 2 of you just need to work on getting quality time together and building reciprocal forms of affirmation. When J came along I think life wasn't too hard for me and the Mrs but then H arrived things were different and I found working on my relationship with the wife was important. Getting time out the house, romancing, doing the unexpected was vital
If I ask you the question what is your love langue would you know what I mean? What I mean is how do you and your wife show and express love to one another. i.e. physical touch, gift, acts of service? My wife is all about gift, don't have to be big gifts just a £2.00 bunch of flowers, a tube of her fav lippy, a single choccy from Thornton’s etc - She is also about physical touch so I make sure I hug her lots, sit next to her and stroke her hair whilst she watches rubbish TV and man is her stuff rubbish! (Have you ever seen Gossip Girl or the Gilbert Girls!). In turn my langue is acts of service, so hoovering, ironing etc I feel loved and valued when she does that kind of stuff or if she cooks my fav tea. When we worked out what our love langue was communication got 100% better.  
The other BIG piece of advice I give all dads is this - YES life is a tad unbalanced for a few year - As dads we def take 2 or even 3 or 4 place but it’s not forever so don't flip out, the grass isn't always greener! Find and engage with the adventure of being a Dad, continue to romance mum and things will get more balanced. 
My youngest starts school fulltime in Sept which takes us as a family into a whole new season and frees up the wife a lot more to think outside the kiddie box - the time really has flown by and it will for you too.
Does your wife have other mates with babies, does she get out the house whilst your at work, does she have folk to talk to who have been there done that? Is she feeling isolated?
When you say she only talks to you when ....... do you truelly mean that she literally doesn't communicate with you on any level other than the baby? Or does it just feel like that? It would help to try and put things into prospective and getting to talk will help that. 
Take the kid down the allotment on a saturday morning, you might find the wife comes too!
Computer games i would say r not the way forward coz it reinforces non comminication. 
Re sleeping on the sofa - sorry to say this but to break the ice on that one you will have to apologise! i'm not saying you are in the wrong but dude as the guy you will have to step up to the plate on that one.
 Start by saying sorry for the fact that you didn't go to bed last night and that you didn't talk this morning.  😉     Tell her that you are just over whelmed and if she butts in and gives it the whole "you're over whelmed what do you think i feel like..." just listen and let her fininsh and say    " babe i'm sorry that you feel that way too, and lets get some time to talk about that but just right now can i tell you how life is for me coz i need to off load about life, work being a dad"  Tell her that parenting is a whole new ball game and that you have found a website that is for dads and it gives you some great ideas etc, it will show her that you are embracing the role. Tell her that you love her to much to spend any more nights on the sofa and that when you married her you signed up spending every night together. 
If she doesn't listen then go talk to her mum and try that avenue. Getting mother in law on side is better than having her against you. Don't get arguementative just explain that you feel tired and want to support your wife, does she have any ideas or wisdom to share! They love that question!!
Mate it will be OK but DON'T go home empty handed stop off at the supermarket and buy a HUGE bunch of flowers!! 😀