If you are having problems with your ps3 there are steps to try an come up with a solution. As far as these solutions I will start here, if you turn your ps3 on and it beeps with a yellow light (Yellow Light Of Death) then you have to do a reflow on this.
A reflow is using professional equipment(at least if you want your system fixed 100% correct) or other conventional methods of heating the GPU (Graphics processor) or CPU (ps3 computing processor) like for example using a heat gun to heat the solder under both of those chips and using thermal grease (Artic Silver) to apply on the CPU/GPU after the chips have cooled down.
I am not going to great detail on a reflow procedure as you can search this to get a complete guide. I do recommend using the penny trip or using a copper plate as this creates more pressure to the chips to keep the system from running the fan to hard, hence another overheat. Now as far as the system turning on a beeping 10 times and turning back off this is a error that is common when the system that was hacked with CFW and going from a retail mode to a debug mode (CEX to DEX Conversion).
This is caused by the syscon checks in the internal memory that you are modifying when you do a conversion incorrectly. In order to fix that problem you must either a flasher (E3, Progskeet, etc.) or if you have a Reader or something similar (PS3 Dongle) you can go into step of recovery this error. I also am not going to give a complete guide on this as all you have to use is search!!!
I would say if these methods don't work then the system is far from recovery and I would consider a ps3 replacement as it would be a lot cheaper then sending this in to Sony. Good Luck and Godspeed!!!!
9 out of 10 times video issues are gpu related. Get it professionally reballed. Your wasting your time with pennies or shims as if they work they are just temporary. Even a professional reflow in most cases only last a couple months. Good luck.