Can't connect to xbox live on 360.

So, I've had this issue with my 360 for a while, when I was on my homepage it would sometimes sign me out of xbox live and sometimes even in a game, all I did to fix it was press the home button and pressed sign in to xbox live and it would work again, but for some reason every time I sign into my profile and I get to the homepage it signs me out after a few seconds and doesn't even let me use stuff like bing and everything looks like I have no wifi connection, but I go into my settings and I have a perfectly good connection, so i test the connection and everything works and it gives me access to xbox live and everything then after a few seconds it does it again, I've tried everything that I've found online, the only thing that let's me use xbox live is battlefield 4 where it some how auto signs me into xbox live but if I press the home button and stay on the menu too long it signs me out of xbox live, and if I go back to my homepage it does it as well, I've done everything I could, I've removed the profile and cleared the cache and added the profile back then it said I had to update my xbox and when the update started it randomly canceled, also, I've had this issue one other time but it gave me an update and fixed it, so I'm guessing if i don't get that update I cant fix it, and I have no way to get the update again, i even tried doing the whole process over again, and I've reset my router, didn't work, even opened up the xbox gutted it, cleaned everything off including the wifi card and put it back together and that didn't fix it, also sometimes when i try to sign into xbox live it gives me errors and sometimes it's one error and sometimes it says I cant access xbox live on this console, I really don't know what to do anymore, I just wanted to start using my 360 again.

:)