[ollopa]

It might help if you post information on the adapters you're trying to use.  It looks like you're trying to connect the TI to a high resolution DVI/VGA monitor.  The TI puts out a composite signal at a low resolution -- the likely explanation is that your upscaler/adapter box doesn't support the low resolution of the TI or that you're hooking up hardware that is totally incompatible.  In any case I doubt that your TI is broken.

If you can find an old TV then your TI should have come with an RF modulator you can use.  The best thing to do is to buy or build a composite cable and plug it into a cheap NTSC LCD monitor from China.  

Something like this would work:  http://www.ebay.com/itm/4-3-TFT-LCD-Fold...SwceNZQjtM

If you need something larger, just beware that a lot of the analog to digital converter boxes don't support the funky timing of old home computer systems.  
Make your own composite cable... http://www.instructables.com/id/DIY-TI-9...deo-Cable/
It will usually work with LCD TVs with composite input but I wouldn't put much faith in random HDMI converters etc.