Turtle is moving slow; lacks excitation. She finally ate a tiny little bit of cooked chicken (she ate that a few times no problem). I was getting worried of the lack of energy due to lack of food.
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I ran out of turtle pellets, so I resorted to feeding it other items, after having consulted a few do's and don'ts here.
I gave her raw carrots (cut in pieces) and pieces of brocoli. I found out later in the day a mess in the tank which was probably her vomit (consisting mostly of pieces from said meal). I concluded that truly her stomach wasn't used to a drastically different meal (she only get pellets usually) so I'm not so concerned about her puking it. I'm more concerned about other pieces I found in the mess, which resembled what I think is pieces of shell. See attached picture.

Full size image: http://i.imgur.com/A6QN0.jpg
Pen added for size comparison. Webcam shot quality.
I'm concerned: is she sick because she's eatinh that? Or is it because I gave her a new kind of food (raw veggies) and this is, somehow, unrelated?
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Mandatoty information:
Size: 5in long
Had it for 2 yrs and a half (since "birth")
Water T= 78-80 (strip thermometer)
100W water heater.
In a 15G tank (no comment), almost full.
Not using water conditioner/other products. Water from the tap.
Large Fluval 206 filter.
Basking temperature unknown. It stands 7 inches away from a 100W incandescent lightbulb.
There is, next to it, a fluorescent lamp ("any" fluorescent lamp for general lighting).
Nutrition: Usual turtle pellets (Nutrifin Max). Attempted raw veggies (carrots, brocoli)
Last time, yesterday (after having puked once): small bits of carrots
Tank is not near a window. Tank is behind me in my office/room.
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