I have a 32 inch Vizio I turned it on and then it turns back off by itself and there is no picture I know I have to replace a board but which one the model number of the TV is M401i-A3

Back - light problem. Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis...
http://electro-medical.blogspot.com/
To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement. To some models sets, the back-light inverter and SMPS section circuit will be integrated at its main board itself. If so; the main board should be replaced. To some models of sets, all these section circuit will be integrated at its main board. If this is the case, you have to replace the main board.

Your signal board (also called, main board) is at fault. This board has all your RF connections,RCA jacks, com0nent connections etc. I have repaired many of these Vizios. Thanks for asking me.Matt of Martins TV.

is the main signal board

Now tv turn on,have a flicker of picture a few sec.than dies,have sound left only?Yes,than the 1 or 2 long LCD inverter boards are dead.Tries websites like Shopjimmy.com,Ebay.com to buy the 1 or 2 long LCD inverter boards for the replacement.

Check the power supply module first.
http://s807.photobucket.com/albums/yy352/budm/VIZIO%20L32HDTV10A/
This one in my pictures has blown power supply beyond repair and bad T-CON board, both are replaced.

Please see my basic troubleshooting guide here:
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide

http://s807.photobucket.com/home/budm/allalbums

http://en.wikipedia.org/wiki/Capacitor_plague
Parts: www.shopjimmy.com

sound more like a remote problem take the batters out and turn it on at the set and see what happens

Ur LCD Inverter board is dead.Replaced this board u will get the picture back.It a long board.Tries Shopjimmy.com,Ebay.com to buy a refurbish LCD inverter backlight board.

Tries unplug,replug about an hour,see if it reset itself.Not than must replaced the signal tuner board.Plasma have this problems alot.

Do you still get sound? If you do get sound, then the problem can be in the backlight inverter board or in the main power supply that supply 24vdc to the inverter board.

Main Board Needs to Re Replaced.