Sorry to make you wait for a response, been a busy day here.
My first thought was that both of those tests failing at the same time could be caused by your motherboard starting to fail (especially if the system has an on-board video card). That may be jumping to conclusions however, as both of these failures can be caused by multiple different issues.
The CMOS RAM test writes data to the CMOS RAM and then tests it to ensure that the information matches. If this system is attempting to write to a section of the memory that is read only then the test will fail even if the CMOS RAM is still good.
With the VESA Full Video Memory test, tests the video memory by writing a portion of data and reading it back. This can fail if the video RAM, video card or motherboard are failing. If the video card is built-in I would make sure that the RAM isn't having any issues also (most on-board video cards borrow from the system memory).