You need to be careful with your terminology - you have a T1100plus you do not have a T1100!! and power wise it appears they are not the same.

From a bit of quick googling I found the following pages, which make it clear that the T1100 is different from the T1100plus.
Note - both pages have "IMPORTANT: T1100, not the T1100 PLUS" in bright red letters at the top.
http://www.minuszerodegrees.net/manuals/Toshi … er%20source.htm
http://www.minuszerodegrees.net/toshiba_t1100 … 1100_pvabps.htm

More info:
http://www.vcfed.org/forum/archive/index.php/t-19849.html

Voltage: Computer DC input - 9VDC, 1.1A (+ = core; - = shell)
Battery: Internal rechargeable NiCD battery pack

9V @1.1A is a bit of a tall order for a DIY PSU.
I would recommend getting your hands on a decent 0-30v 2A bench power supply, preferably with adjustable current limiting.
If you then decide to build your own PSU, then you are looking at a linear design (use a pay attention to minimising heat dissipation, and fit a suitable heatsink on the regulator),
or a switching design. Note that the adjustable switching PSU modules from china are notorious for promising to deliver 2 or 3 amps, but then letting out the magic smoke when you pull 0.5.
You could feed either from an existing 12VDC supply thus avoiding having to dabble with transformers and 110 or 240V AC.

Note that I got this info by googling for

1"T1100plus" adaptor voltage

9VDC @ 1.5-2A is a common supply for portable DVD players - find one in a bin at a thrift store and change the connector.

Well, quick update, I didn't need a search engine to find the voltage, it's printed on the device. The problem is finding an original adapter, which I had hoped to do. It would be nice since at least one of these will end up in my collection (probably a few since I found the Zenith in the bunch). 40 minutes of "quick googling" netted me nothing but expired eBay auctions and lots of 19.5V adapters in the search results, binging and duckduckgoing too.

Secondly, 1.1A is not especially unusual or powerful, so I don't think it would be hard for a DIY setup, I mean you could make one out of a PC PSU, of which I have tons.

But thirdly, I think I came to the same conclusion as dr.ido - 9V wall-warts are common, and looking through a few it looks like 9V+ 5.5mm center-positive is *extremely* common. I actually have one but the amperage is too low, I looked *those* up and they're easy to find. I might rig it to a short extension given how inconvenient fat wall-warts are,

I may never see an original one (you may have noticed most old laptops for sale don't have power supplies), but a non-original substitute should not be hard to come up with. Heck there seem to be new ones with the correct specs for <$10. It seems unlikely I'll be building *this* PSU from scratch - but I would still someday like an original, for collector's sake.