How do I connect my PC to both my monitor and TV: particularly with a splitter?

I assume you mean VGA port?

Idf you only have one port, I’d suggest that a splitter won’t work – as I understand it, VGA is only designed to address one display per adapter.

The simplest solution would be to just buy a cheap (like $20 – $30) graphics card

Thanks the100thmonkey.
Oops, I forgot to mention: that when I plug directly into the TV
– without the splitter-
I get the same problem.-

And this is why I like my old Radeon 9800XT. It may be a little old cannot support DirectX 10) but it has VGA, DVI, and TV out, and the chops to run different desktops on each.

I’m pretty sure that you could find one (or something similar) really cheap.

Thanks to all, and I’ll consider both of your comments.
I seemed to have had some progress here

@Pata – that seems largely correct. You might find that older video cards don’t support as many different resolutions as modern ones.

The name/model of the computer and the TV would be helpful for us to know.

You can use a VGA Splitter/Converter to do the job. I use a GEZ-1000 by Grandtec.