I have similar problems in an HP laptop, first thing I do is to use a different USB Flash Memory, because first one I used was probably damaged.
Second thing, try without graphic acceleration, my HP doesn't support GL and I have similar symptoms, the same Elive release in an oldest Acer 5310 supports GL.
And finally, you will probably have damaged sectors in your HDD. Release 3.0.6 of Elive will inform you after booting. My HDD it's damaged into the HP and sometimes I got the same symptoms that you. After next reboot Elive shows me that I have some new damaged sectors in my HDD. I use Unison tool at Elive to have my data continuously synchronised between 2 computers so it's doesn't matter to me that my HDD is dying. Anyway, I have a clean install with reiserfs and crypted partition and Elive proposed me to erase all my HDD with zeroes to isolate as much as possible the damaged sectors; It's very risked and you can lost your HDD, but I do it and my HDD works better, but sometimes I have new damaged sectors that appears.
Try also to install Elive WITHOUT any graphic acceleration.
Hope it helps you and be free to ask for any doubt.