XPS 8000 with Nvidia GTS 240 card - drive two displays?

Trying to get dual monitors going on an XPS 8000. It has an Nvidia GTS 240 graphics card with dual DVI-D ports and a smaller display port. No native HDMI. I can plug a Dell monitor into either DVI port and it will display correctly. But if I plug a DVI to HDMI adapter (Nvidia branded, it came with the computer) into either port (either alone or in conjunction with the monitor), and then plug an HDMI cable between the adapter and a Sony Bravia flat screen tv, I get no picture on the tv. What can I do to get this card to display to the tv? Or do I have to upgrade to a better card with native HDMI support? The tv does have a VGA port, but I already spent the money on an HDMI cable and attached it to the wall with cable clips. Plus, the output from HDMI will be better quality than VGA quality. I would honestly rather upgrade the card than downgrade the video quality.