I have a problem with OpenSUSE 12.3 64bit version. My dekstop icons keep disappearing after every reboot. To show them, I have to delete the current desktop activity and create a new one. After that, all my desktops icons are there again.
No. If I remember correctly, I once run openSUSE 12.3 with KDE, but I can not remember I ever experienced what you experience. As, logicaly, I have no 12.3 available any more, I can also not try to reproduce your problem.
If someone is throwing untested or supported kernels into the mix it is very hard do say where the problem is.
I suppose you need to start with the video. What card/chips and what drivers? If using proprietary drivers were they recompiled for the new kernel? Do you have the kernel source for the new kernels so you can compile the drivers? If using the open source drivers then it is possible the kernel changes may break some of the external video packages. It is possible that you may need to recompile some stuff for the new kernel.
Also are you sure that is is openSUSE and not SUSE?? These are different and do have different support times.