Blowing Up A Video?

I have a 15.6" notebook PC and have had Slingbox connection, providing me with a
4" x 4" miniscreen, with good resolution. My PC screen resolution is 1366 x 768
pixels. If I buy a larger monitor(around 20-24" with a choice of 1920 x 1080 or
1600 x 900 pixels) and attach my VGA cable - my PC has no HDMI port, will the
blown-up picture lose any, little or a lot of resolution?
Blowing up the current miniscreen to full screen loses a lot of resolution!
My video card,BTW, is an AMD M860G-w/ATI Mobility Radeon 4100 card. Would getting a new, more powerful card help?