adding more RAM might help.
No, it won't. RAM isn't the answer to everything.
The CPU has nothing to do with this error. Yes, it's an ancient processor that will probably run Skyrim horribly, but it's not the source of the error. "Failed to initialize renderer" is a common GPU bug, and is usually caused by broken/outdated drivers. MAKE SURE that before you install new drivers, you not only uninstall the old ones either through the control panel or the card's own uninstallation software, but run a program like Driver Sweeper to clean all remnants of the old drivers.