Going to attempt a reball, some questions

@euler something going on with your comments on here. Somewhere along the line you ran into issues with it getting deleted 1-0 times as spam, so it dropped your reputation points significantly. I tried to reverse it but can not do it for all. I'll let @kaykay know and hopefully she can get this straight.

In the meantime, the hot air station will be difficult to use since it gives you the temp at the nozzle but not at the chip. So, poor control would be the outcome. Problem with such hot air stations is that you can't evenly heat up a large area. The outcome would be that you are burning one area, while the solder has not yet melted on another. You might also run into the board warping since you do not have a preheater. There are large IR with preheaters and tight temperature control for this. What you are really looking for is something like this. It provides the proper preheating and you can control the heat to the IC and limit it to the IC. Even tho there are no real alternatives to using the right equipment and given your situation of not being in the US (not sure where you are) you could consider using the station you were looking at, adding something like this and using a thermometer with thermocoupler like this. Use a griddle as preheater.

Again, really not advisable but if it is the only option you have then you can consider it. Chances are minute to get it done properly.

Now with all this said, you do need to remember that these failures may not be caused by the solderballs etc. If your processor is a flip chip design and the issue could be the solder bumps between the IC and the substrate. A reflow might fix it for a while but even reflows are very limited. YLOD (as well as RROD on a Xbox) are caused by the design of the processor, not necessarily by bad or cracked solder joints. The key to this is the design of the processor which is a flip chip design. The proper definition of that can be found at Wikipedia "is a method for interconnecting semiconductor devices, such as IC chips and microelectromechanical systems (MEMS), to external circuitry with solder bumps that have been deposited onto the chip pads." So what happens is that the chip heats up (due to poor design of the ventilation and heatsinks of the console. Does not matter if it is a PS3, a XBox or some of the Mac laptop's) and the bumps that connect the chip to the substrate lose contact and your chip (in this case processsor) fails. The heating of the chip for the reflow actually reshapes (most of the time) the bumps to the point of making contact again. That is the reason why some reflows just do not work. The connection between the IC and the substrate has absolutely failed. In those cases you will need a new processor. Not the most scientific explanation but I hope it makes sense to you.

General guidelines for a good profile would be something like this:

Temperature ramp up 1ºC/second

Peak temperature should be 200C to 210C

Remain above liquidus (183C) for 45-75seconds

Do not heat any packages above 220C since this will most likely destroy the IC

Here is a good document that will help you with the profile as well. BGA-Reflow-Rework.pdf You now see where it would be very difficult to achieve this type of tight and timeline dependent profile with a heatgun.