You wrote about internal memory being low. Did you uninstall as many apps as you could?
The issue with failing boots is a pretty widespread Android issue when memory is low. That issue is not a Samsung one and some folk are only beginners with this OS. That is, they need others to explain to them that it's a common issue and to uninstall more apps.
I have a phone which is Samsung Galaxy Y Duos and I had it for almost half a year. My problem is that whenever I boot up my phone, it usually load and prepare the apps, scan my SD card for media and other files etc. but after all of these when I tried to unlock my phone by swiping the screen, I couldn't unlock it and it gets stuck or even that I had unlocked it, the screen gets stuck and all of these gets my system to reboot again for two times and it powers off. I've managed to switch on my phone again and it gets back to normal. This problem is persistently occurring and I don't see anything or any problem that happened or I have done to my phone. My recent activities before this issue happened was I opened the Sysdump(by dialling *#9900# and opens it) and I select "copy to SD card" and it transfers the dump files to my SD card so that it decreases its usage from my internal memory as it is so low. Other one is my phone is rooted but I'd done it successfully and with out any problems. I also often switch off and on my phone for many times in a day for other reasons. Please send me your solutions and tips to cure my phone's issue. Thank You.