Im loking for the output adapter cable for my monitor, name-ADV1901B, MODEL-F192, 15V---4A, Were can i foud that type of adapter?

Search on amazon. Don't know your location, but example is below:
High Quality New 12V 5A AC Adapter For LCD Monitors and LCD TVs With...

First of, a little bit of explanation.
VGA = analogue
HDMI = digital

The answer seems to be in your question.
it reads "VGA to HDMI". These cables or adapters doesn't work the other way around. I am guessing your cable can only support vga output to HDMI input. And your setup is HDMI output from your computer to vga input to your monitor.
Solution:
Try and find HDMI to VGA cable or adapter. This is expensive.
If your computer has a vga output, use this with vga to vga. You won't get a better resolution by using HDMI to vga.
Or are you stuck with only HDMI output?
There are adapters for USB to VGA too. This could be less expensive. I have one for my friends Apple Air. I am not a "i" fan so I do not have much experience on Apple.

Hope this helps.

12vdc adapter about 4a.
http://12vadapters.com/adapter/power-supply/12v/for-lcd-screens/mag-innovision-lt765s-3.html

Watch out for bad solder joints on the 4 inductors in the backlight inverter board.

Basic LCD monitor and TV 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://www.fixya.com/support/r7406380-tv_training_manuals
Failed TV and Monitors: http://s807.photobucket.com/albums/yy352/budm/

Learn about bad caps: http://en.wikipedia.org/wiki/Capacitor_plague

Capacitors kit: http://lcdalternatives.auctivacommerce.com/ he can make you a set of caps for you.

Or www.digikey.com just make sure to use caps with low ESR, 105c, high ripple current, long life rating such as PANASONIC FM or FC series.
Please leave rating if it helps.

The power supply AC adapter power cord is the same as used for PC power cord, local PC repair shop should have them.
Or you are looking for the AC adapter is 12v 4A power adapter, try Ebay

http://s807.photobucket.com/home/budm/allalbums
http://en.wikipedia.org/wiki/Capacitor_plague
http://www.badcaps.net

http://www.allelectronics.com/make-a-store/item/PS-1240/12VDC-4A-SWITCHING-POWER-SUPPLY/1.html

You do need to find out what kind of the connector you will need.

here's a link for one on ebay: http://cgi.ebay.com/Power-Adapter%3a-LG-Flatron-575MS-LCD-Monitor-(12V-4A)_W0QQitemZ370109233697QQcmdZViewItem?rvr_id=&itemid=370109233697

you can also google the following: LG flatron 575ms power cable

there should be several listings

Hi. I had a similar problem, but cured it by getting a new PSU with a larger rating 4A. The digibox is now perfect, and earlier problems of lockups were also fixed. I suspect the original PSU wasn't really man enough for the job.

The new PSU (originally for flat screens) cost £9.99 incl postage from Ebay, from the seller AC Adapter Specialists. Delivery was prompt. Type is 12V 4A tft lcd screen monitor ac adapter. Check the DC outlet plug matches your digibox.

you can use any laptop AC adapter DC output-16V and 4A (current). if its jack size natch your laptop DC jack.
if the adapter DC current less than 4A (over 2.5A at least) you should only make the battery charging without laptop turn on!!!
please take a rating let me know how much helped you thanks!

you need output to be 12v 4a