Like many others, I am also experiencing this standby-of-death (SOD) problem: the lights in the buttons under the screen turn on, but the screen itself stays black. I have found out that it has to do with switching from 3G to 2G networks: the problem occurs after I have been at places where there is no 3G signal, but only 2G. For example, after a car trip or when going into the basement.
A workaround for this problem, is to type the code *#*#4636#*#* in the dialer. You will then end up in a hidden menu. By choosing "Phone information" (first item) and then scrolling down in the next screen, you can change the "Preferred network type". By default, it was set to "WCDMA preferred" on my phone. After I changed this setting to "WCDMA only" (so, 3G only), I have not seen the SOD issue anymore (for 4 weeks now, before it happened almost daily).
A disadvantage of this workaround is that the phone will never use 2G anymore. So, when you are at a place where there is no 3G signal, you will be disconnected (i.e. you cannot receive phone calls). As an alternative, I have now reverted the setting to the original value ("WCDMA preferred") and I have installed an older radio image (version 32.44.00.32U_5.09.05.30_2), which is considered to be more stable by many people. I'll test and see whether the problem reoccurs. If the problem stays away, it is apparently a software (radio image) issue. If not, it must be a hardware issue.
Anyway, if anyone has additional information about the root cause of this standby issue, please let me know!