There's a lot going on in your question.
The converter that you linked converts DVI to VGA. The usefullness of this product is VERY limited. The only time you would need this is when you have DVI-D (digital only) and need to drive an analog display. Most DVI outputs are DVI-I, which include both digital and analog signals. All that's needed is a simple adapter to drive VGA from DVI, and those adapters are commonly shipped free with video cards. I have a whole box of them sitting in the corner.
Besides, you want to go from VGA to DVI/HDTV. ATI has a VGA to HDTV adapter (
http://shop.ati.com/product.asp?sku=2537968 , $29) that may do the trick. You should use the Catalyst Control Center to set it up (switches and mode). Be careful using these because they can damage your HDTV if you use the wrong settings. I don't know if this adapter will work with the mobility version of ATI's graphics chip, but it's worth a try.
Note that this is an adapter, not a converter. You should avoid converters that go from VGA to DVI. they must perform internal scaling and/or scan conversion and the output will be sub-par. Also, ATI doesn't support 16:9 aspect ratios in VGA mode, so you probably won't get the correct aspect ratio on your HDTV using a converter.
The only I know to get DVI output directly from a T60 without buying a dock is to get a PCMCIA or USB video adapter. But these will be too slow to drive an external HDTV. It's possible for someone to design a cable to hook up to the dock connector on the bottom of the T60 that gets DVI output without a dock, but until right now I don't think anyone's ever mentioned it.
If the $29 ATI part mentioned above doesn't work, your next best options (and most expensive, unfortunately) are to get an Advanced Mini Dock (AMD) or Advanced Dock (AD). AMD will give you DVI-I output, but it may not be compatible with many HDTV's. Broadcast video is very different from computer video, even in the HDTV world, and many TV's won't handle the computer signal very well. Your best bet is to get an AD and put a PCI-Express video card in the expansion bay that supports HDTV video output. There are many cards that do this (Matrox APVe, for example
http://www.matrox.com/mga/workstation/v ... _apv_e.cfm). I have the APVe card and it fits in the AD just fine.