Have you tried any boot parameters (sometimes called 'boot cheat codes') when you first boot the LiveDVD? See the (slightly out-of-date) SL Wiki page Visual Tour: Part 1 Booting Sabayon Linux
for where to enter boot parameters, and the page Cheat Codes
for some boot parameters to try. If worst came to worst, you could try using the xdriver=vesa boot parameter to try to at least get SL installed to a usable display, and from there try to install an nVidia driver that works for your GPU.
It's very difficult for anyone to help you because you are using new hardware. There may be very few if any other SL users with your hardware, or even with netbooks or nettops using the NVIDIA ION LE GPU.
A cursory search of the Web shows that there are
people running Gentoo on the Acer Aspire Revo (e.g. My Gentoo/Linux Wiki on Acer Aspire Revo R3600
in Japanese), so your cause is not entirely hopeless, but unless someone who knows or uses your hardware wants to reply to your plea, you are up the creek without a paddle.
From what you describe, it could be a video driver problem. I have no idea about nVidia GPUs, but googling your hardware "NVIDIA ION LE Graphics" I found the following article NVIDIA ION Linux Performance
which states that it is based on the nVidia GeForce 9400M GPU. So trying a Linux driver that works with that GPU would be my first guess. Doing some more googling, it looks to me like the driver you need is nvidia-drivers
Can you get to a TTY console? If you press Ctrl-Alt-F1, Ctrl-Alt-F2 up to Ctrl-Alt-F6, do you see a text console with a Linux login prompt? If you can login there as root then you can check if you have Internet access (e.g. by pinging) and, if so, do some remedial work such as attempting a text install (see the above-mentioned Japanese Web site, a lot of which is understandable as it shows the commands and console output -- for example he merged (compiled/installed) nvidia-drivers-190.42-r3 with USE flags acpi gtk (multilib) -custom-cflags).
Perhaps someone who uses nVidia hardware can take it from here and offer you some more-detailed advice.