How do I get my graphics card to output a hdmi signal to my HD tv via a hdmi splitter box?

Hi, if I connect the HDMI cable from my computer graphics card (ATI Radeon 4800) directly to the HD tv, I get the desired picture (duplicate/ extended). However, I've just invested in an old PS3 which also needs a HDMI socket and as my tv only has 1 HDMI socket I bought one of the HDMI splitter boxes. This works great for the PS3, but I can't get the computer graphics card to send a signal to the tv via the splitter box. Apart from buying a new tv, any advise or suggestions'd be appreciated. Thanks