About jpg
It's not photoshop that limits jpg to 8-bit imagery, it is the jpg specification itself. There is currently an initiative underway by Microsoft (with Adobe as a partner) to revise the jpg standard with a new jpg+ that will allow for lossless jpg and well greater bit-depth.
About single image "HDR"
As has been pointed out, HDR means high dynamic range and that means the range between black and white; 0,0,0 to 255,255,255 in an 8-bit image such as jpg. You can't produce an HDR from a single image no matter what you do. The range of the image remains the range of the image. To nit-pick, no image displayed as a jpg is really an HDR image, it is an HDR image tone-mapped to give a broader range of luminosity than the original.
Psuedo HDR
There are any of a number of ways you can do this. If all you have is PhotoShop you can create the same effect, more-or-less, by creating 3 layers and adjusting the layers differently; one dark, one where you think middle gray is and one light. Put a mask on each layer and then selectively remove the mask. I do this all the time in the context of doing a burn or a dodge. I seldom use the dodge / burn tool as it is destructive. I creat a "burn" layer and a "dodge" layer with inverted mask and then use a low-opacity brush to reveal / hide what I don't like. This really what you are trying to accomplish when you try to do an HDR from a single photo.
But creating a pseudo-HDR by hand is an immense time grabber. You'd better really want to do it.
About PhotoMatrix
I think it works pretty well and it is easy enough to use once you understand the steps. My first real attempt was horrible. I couldn't figure out what was wrong, why I couldn't get a descent HDR. Two words: dumb user. After "generating" the HDR you have to tone map it to get it to look good on a monitor; duh.
YUCK
Just be careful with HDR and tone-mapping. 90% of what is produced is very evident that it was tone-mapped and looks bad to anyone not an affectionado of unreal / over-processed / over-manipulated images. A light touch can produce some intersting photos but go just a bit too far and you've got 1960's velvet paintings of Elvis.
Charlie