If you unplug the HDMI cable (or is it the DVI cable?) the VGA port will work. Obviously that doesn't help you run all three at the same time.
1) What's your budget for a new GPU
2) Do you play games (if so what games) and what monitor do you game on. (your 24" monitor or TV with 1080p screen is easier to push than the 2560 x 1440 screen on the Koran monitor in games)
3) Do you require any specific combination of ports?
The 7770 for $100
is an inexpensive card for 1080p gaming.
The 7850 for $170
is a good place to start if you're gaming on your 27" korean monitor.
All AMD 7xxx cards and Nvidia GTX 650
on up support 3 monitors.
Main: i5-3570K, ASRock Z77 Pro4-M, Asus GTX660 TOP, 120 GB Vertex 3 Max IOPS, 2 TB Samsung EcoGreen F4, 8GB 1600MHz G.Skill @1.25V, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Hand-Built Wood Case