Other than that, try giving the thing some relief from dust - take a hoover to the vents on the sides and the back (Or just blow into them).
Maybe it could be an overheating problem. How old is your 360? It wasn't that long ago that they were notorious for overheating so much that they melted it's own soldering inside - Making the console **** up and eventually giving the red ring of death.
Is it making any odd noises?
Keep doing it, stress the 360 as much as possible, eventually you'll get the three rings of death. Keep stressing it some more to ensure they pop up 'on demand', i.e. every time you start up the console, get it replaced if you've had it less than three years.
This happened to me - the 360 would work until freezing up with audiovisual artifacts, first about an hour into gameplay, then progressively sooner until it would lock up within 5 seconds of startup. I got it replaced for free.
*This is assuming you keep the console well-ventilated, of course.
The 360 has had heat issues, historically...they tend to lead the the three rings of death issue after a while, try the following:
Make sure it is in an area with decent airflow around it.
Try a quick hoover - stick the nozzle of the hoover on the vents of the xbox - if you can get some then clean compressed air is good to blast into the vents first to free up the dust.
Apart from that then there is little you can do. how old is it? if it is within 3 years of purchase then the 3 rings warranty is still in force (I think check first), so it might be worth driving it hard to see if it does go the whole hog and die, then replace under warranty...risky option.
There are several links on the web on how to do some DIY maintenance on the board to increase the cooling levels - basically strips the board, adds some better heat transfer compound and then re-assembles....again a bit risky.
I occasionally get a grey/ green chequered screen when I boot my xbox up. When I say occasionally I mean maybe once every 3 months or so. Sometimes it goes away after re-booting a couple of times but like the other day it stayed for a good few hours before going away by itself!!
No red ring of death or anything like that and I've made sure to check all scart connections etc. Anyone else experienced this?
Tis on its way out, mine done this a few months ago.
They'll repair(or give a retail recon one) if for free if it is less than three years since purchase or if less than one replace it.
Over three and you either have to pay for the repair or buy a new one.