I have a Toshiba 23hlv86 that comes on for about 15 seconds then shuts off. Any help would be appreciated

What is the problem you faces with this TV. Provide more details, please.
If you wish to get some details; check the site linked here. Pull up older posts. Surf the site with patience. http://electronicshelponline.blogspot.com/

upgrade the BIOS

does it shut down and then just start right back up? If it does then press and hold the power button and make sure it shuts down all the way. Then take the battery out and press and hold the power button after the battery is out for about 5 seconds. Then let it sit like 10 - 15 seconds. After that put your battery back in and turn it back on and see if this solved your problem. I think its in a loop to make it keep restarting. Let me know if this helped. Thanks, Herb Stacey

It does not get any video signal. That is all. Check all inter connections, tuner and other related components.

The power supply for the back-lights inverter board, or the inverter board, or the main board not sending the signal to turn on the back-lights. You need troubleshooting to narrow it down.
Please read my guide to get basic understanding first.

Basic LCD monitor and TV troubleshooting guide:
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide
http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting
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
Parts: www.shopjimmy.com
Capacitors kit: http://lcdalternatives.auctivacommerce.com/Default.aspx he can make you a set of caps.
Or www.digikey.com, just make sure to use caps with low ESR, 105c, high ripple current and long life rating such as PANASONIC FM or FC series.
Please post back what you find.

If this is a LCD Flat Panel TV, the LCD Panel it self would probly need to be replaced.
Skyassoc

heat comes on for 15 seconds then shuts off

A lot of recent Toshiba and Vaio computers have had some issues with intermittent fan control issues. Updating the BIOS from the manufacturer's website should solve this problem.

Try unplugging your CPU and wiping any accumulated gunk which may have oxidized there, causing heat buildup. You have, of course, cleaned all the accumulated dust off your fan blades?