Paul, firstly you need to know that there are people out there who can help you. Go and see your GP (ask for a long appointment), lay it all on the line and ask for a mental health plan. Once you have the mental health plan in place it will entitle you to see professionals such as psychologists and it will be covered by Medicare which will help when money is tight.
In order to get the most out of it, you have to be completely honest and upfront with your doctor. I know that men can tend to bottle things up, put on a brave face and in that way can be their own worst enemies.
When the black dog of depression hits you it can seem like you are in a pit so deep that you can never see the light or climb back out but you CAN, with professional help.
You have those boys and you are their father, they love you unconditionally and need you in their lives for as long as possible, long enough to watch them grow and guide them to adulthood, watch them have kids of their own and bounce those grandkids on your knee. If you were to do something drastic now, their lives will never be the same. Ever.
Depression is a horrible thing and not just for the sufferer, often those around have no idea what's going on and just see this person who is different that the one they know, a person who is withdrawn all the time because the focus with depression is always inwards. If, like most people you aren't sharing this with your partner then perhaps she doesn't understand why you have pulled away from her and it has made her angry....this may explain why she's spending so much time with her girlfriend...to get the support she needs to try and understand without having the benefit of the full story of what is going on with you.
Can you ask a relative to take the boys one evening so you and your partner can spend some time talking. Be really honest with her about how you feel. Reassure her that it's nothing she has done or not done. Ask her to help you get through it, together.
The the first available opportunity go and see your doctor, take that first step on the road to recovery.
In the meantime try
http://www.menshealthaustralia.net
Even though you may not see it now, there is light at the end of the tunnel, sometimes you just need someone to help you through until you can see it.