WP VPS problems

I have a problem with my blog, gernte.com, I switched from UnoEuro.com, sharedhost, a few months ago because the page had grown from the sharedhost’s – the VPS is faster and better, and of course more expensive. It is not the problem. Everything worked on that server.
The problem is that after I switched to my own VPS, the page can not update anymore, nor can it show news from www.remarpro.com or install plugins, themes through the backend. Scheduling post does not work, either.
The problem must be something with PHP, which means that it can not contact other servers through PHP. I can not find anyone with the same problem, nor anyone who has solved the problem.
Update menu shows that everything is “up to date” – but when new updates come, it will be shown with a small number next to the menu item to indicate that updates are available, this resets when I try to update.