Insignia 27" sound and video was going out replaced power Supply and now just the video goes out after 20 min to 1hr

It sounds to me like the power supply for the back light needs to have new capacitors installed. TV's are now manufactured to fail shortly after the warranty runs out! See if you have a friend that can do the repair for you.

Capacitors in the power supply are going bad

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

Sounds like power supply regulator board fault. Check all the electrolytic capacitors for any leaked or bulged one. Contact any service technician. If you wish to get some details; check the site linked here. Viewing it in "Mosaic" or "Magazine" will make surf easy. Surf the site with patience. Pull up older posts. Do asearch by type in the brand name of your device at its search box.
http://electronicshelponline.blogspot.com/
It will be best to replace the power supply regulator board as card basis.

sounds Like a power supply issue and u should always have speakers connected before u turn on maybe power supply is about done open case an check for any leakage on power supply unit or small cracks on it ...if so its pretty well done
Never good to power up without speakers connected can blow power outputs

possibly, it sounds like there is a capacitor in the power supply not holding charge anymore. Or it is loosing hold of the charge once it gets warm.

Service manual; http://www.my.electronicshelponline.com/uploads/Insignia_Xoceco_LC-37HV41_NS-LCD37HD-09_LCD_TV_SM.pdf

Power supply is only $32.
http://bestbuy.partsearch.com/Model/Best Buy Company Incorporated/Insignia/NSLCD37HD09.aspx?SearchTerm=True

http://s807.photobucket.com/albums/yy352/budm/Insignia NS-LCD37HD-09/

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

Failed TV and Monitors: http://s807.photobucket.com/home/budm/allalbums

The vertical deflection has gone out. Put it in the shop.

look for cold solder joints on primary side of power supply

the most common item that fails with all LCDs is the power invertor or power supply, and that sounds like what your set is needing is the capacitors have possibly failed on the Invertor