Won't turn on rightaway - ViewSonic VA902b 19" Monitor

I would look for bad caps with leaking/bulging tops or seals. 702 is similar to 902
If you are going to DIY and have proper tools and know safety precaution then please read on:
Most common failures in the LCD monitors are bad capacitors (bulging top/seal or leaking) in the power supply (they should be replaced in a set), blown fuses; poor solder joints, failed inverter circuits (blown fuse, shorted transistors, shorted/open transformers), bad lamps (poor solder connections or worn out lamps). You will need to open it up and inspect the inside, see example of failed VIEWSONIC monitors to get some ideas what to look for: http://s807.photobucket.com/albums/yy352/budm/
Post back what you see inside so we can guide you further and it will help out other people in the future also.

Basic LCD monitor troubleshooting guide:
http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide

http://en.wikipedia.org/wiki/Capacitor_plague
Learn about bad caps: Capacitors kit: http://lcdalternatives.auctivacommerce.com/ he can make you a set of caps for you.