Increasing Video Card Memory

You can do this by going into the BIOS of the system, for most boards, it is under the "Hardware Peripherals". You can increase it from there, but only to the limit specified by the VGA's specification. Meaning, you can't increase a 64MB onboard card to say 256MB.

There's really not adverse effect as such, but the only consequence would be lesser total memory for the system. If you considering the increase because u game a lot, then get a dedicated VGA card.

Let me go through some basics about video solutions:
There is essentially 3 options:
1. Onboard graphics with shared memory (ie the video uses some of the system RAM), these are usually low end GPU's(Graphics Processing Units) and any RAM allocated to the video is not availiable to the system as RAM.
Eg: A 512MB system with onboard video using 64MB will give you 448MB system RAM.

In some cases with this type of video the BIOS will only let you allocate upto a certain amout of MEM to video (eg 32MB) but will dynamically use more free RAM as needed when running more demanding apps/games.
This solution can only be upgraded by adding a seperate video card and disabling the onboard video in BIOS.

2. Onboard video with its own seperate memory.
 This is more like a seperate video card built into the motherboard but usually using a lesser GPU. These can only use the mem they are built with (eg 64MB) and can only be upgraded in the same way as soution 1 (ie replacing with distinct Video card).

3. Seperate video card plugged into a PCI/AGP/PCIe slot and having its own RAM (eg 256MB).
 To upgrade you can overclock (not always a good idea) or replace with new card (best) but you can't increase the cards RAM.

Hope this helps in some way.
Cheers!

No AGP and PCI slots? That's rather strange.

I really doubt that the system doesn't have atleast a PCI slot, but if it really does not have any, then sorry to say, but you just have to stick with the VGA card on board.

The option left is just for you to go into the BIOS and increase the memory (usually, this is done under the "Hardware Peripherals" option in the BIOS) to the maximum available - 64MB

Confirm that your board REALLY does not have these expansion slots, or can you get the system model/board model # so that I can help you get further details on it?