Problems with signing in to Xbox Live and Xbox 360 starting up very slow. HELP!?

I have had an Xbox 360 since 12/25/2006, and an Xbox live profile for a bit over a year. Just very recently, I developed two problems with the 360 and Xbox Live.

1. I cannot sign in to Xbox Live nine out of ten times I try. There is nothing wrong with my connection, and I use Verizon FIOS internet. My xbox is connected via Ethernet cable to my router. I cannot see why this problem just occured. Once I get into to Xbox Live, it runs great, as expected (perfect connection usually). But it sometimes takes me 15 minutes of experimenting to get into Xbox Live. Can anybody help?

2. When powering on my console, there is about a 30 second start-up time - it was instant until a week or so ago. There is also a 30 second "lag" when going from test connection back to the game I was playing (Call of Duty 4), and some other times around the Xbox menus. But once I'm in game, no problems. Can anybody help?

Thank you all very very much who can help me. I truly appreciate it!

Problems with signing in to Xbox Live and Xbox 360 starting up very slow. HELP!?

Sounds like the console

Problems with signing in to Xbox Live and Xbox 360 starting up very slow. HELP!?

you can do 1 of 2 things

you can either send it to microsoft and get a replacement

or u can do the towel thing that is used to solve the red ring of death by covering ur xbox with towels and leaving it for 15-20 minutes.look it up in youtube it shows u the towel thing and stuff.