Windows Phone issue: Unable to connect to Windows Live ID service is unavailable

I bought a Nokia Lumia 800 a few days ago and I'm facing problems with WP since then. The very first day I got an error while downloading an app. from Marketplace. The app. was Fantasia Painter. The error was: The Windows Live ID service is unavailable at the moment. So I did a reset as I had no other data and no apps. installed on my phone. But after reset Nokia Apps were not available for my Lumia 800. I was unable to download any Nokia apps. on my phone. So I took it back to Nokia Priority store and said that my internet connection is too slow and fixed the problem. Everything was fine until today when that error showed up again. I can't download anything from Marketplace and cannot use other WP features related to Windows Live ID(Bing Search included). The commonly found solutions aren't working and I don't want to reset the phone again(4th time) as I've got many apps., songs and games on my phone. How can I fix the problem? (And my internet speed is not very slow, it is about 1Mbps. And, my PC has got a dead motherboard so I can't connect to Zune without going to a Cybercafe) I was trying to download Fantasia app. today when I got that error again.