Samsung S3 Cannot Enter Recovery Mode, and Can't Boot Up Either I'm trying to fix a Samsung S3 which has been stuck on the boot logo continously, and cannot boot up. The phone keeps displaying the logo (which says "Samsung" and the phone model) when the power button is pressed, and it will not shut off unless I remove the battery.

My first attempt at fixing this was to enter recovery mode (holding the power button, volume up, and home button at startup), but the diagonistic menu didn't show up. Repeated attempts of removing the SIM and SD cards first also resulted in failure... nothing happened when I held those keys down.

Strangely, download mode (holding the power button, volume down, and home button) worked. The screen lit up with a prompt to enable the mode. However, the phone isn't mine (I'm just helping someone fix it) and they don't want to reflash their firmware if possible. I have done rooting before and understand the process, but since it's not mine the risk is too great.

Will reflashing the firmware fix the problem? Is this a hardware or a software issue? What does it mean if I can't enter recovery mode?
This is most likely a software issue, but you can't be 100% sure until you flash a new ROM and see if it works. If you find a stock ROM, then it won't void the warranty, so it should be safe to try. 

You can find a lot of stock ROMs here.