One thing you can give a try is the TVWizard that is bundled with the Intel graphics driver. Download the latest driver from http://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=19335 for the 32 bit version, or http://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=19337 for the 64 bit version.
Unzip the driver file and run the setup.exe to install the graphics driver. After the driver is install open the folder the driver was extracted to and in the Graphics folder you will see a TVWSetup.exe, this is the installer for the TVWizard. Install the TVWizard.
Now you will have the ability to adjust the various settings to optimize the TV image. To start the TVWizard, right click on the desktop and in the context menu you will see the Intel(R) TV Wizard. Click to launch and the rest is self explanatory.
HDMI is not an interface exclusive to computers. Your TV doesn't support computers because it treats every signal from the HDMI port the same way and the problem is called "Overscan". Thats the reason why you don't see the edges of your desktop on linux as you mentioned. Instead of writing a large text what "Overscan" exactly is, i would rather like to point you to wikipedia.
Some TVs have a special HDMI port dedicated to be used by computers or need to be told in their onscreen menu on which HDMI a PC is connected (or both). Many Samsung TVs for instance ask you to connect your PC to a specified HDMI port AND set the name of the port in the TVs menu to "PC" so the TV knows: "I shouldn't hamper/optimize/change anything on the videodata I get from this port"
But this isn't helping your initial problem: If i should guess, then the windows driver gets no information from the TV about the TV and therefor doesn't detect it as valid monitor. I guess thats another reason why Thoshiba states the HDMI isn't meant for computers: it doesn't provide information about itself as most DVD/Blueray/HD-Player wouldn't ask for them.
Linux on the other hand doesn't rely on this and is set via the xorg.conf which tells the driver how to "talk" to the monitar exactly.
The tool mentioned by Robert_U might help you, but if i'm correct with my guess i doubt so.
The problem in this case however is the TV which doesn't fully comply with the de facto standard, not the graphics card.