What parts can I use to make 110V DC from 4 D-size alkaline or NiMH batteries?
Yes this is possible, but not practical.  Since you don't need isolation (the whole thing, batteries and all is insulated), a basic boost converter could in theory do this.  100 V out will mean you have to select parts carefully.

At that voltage you're not going to find a integrated buck converter chip, but you should be able to find one that can drive a low side switch.  The 100 V is then divided down and fed back into the chip, which should have a fixed internal reference voltage to compare this feedback input to.  The chip therefore never sees the high voltage directly.

However, the real issue is the current this will draw from a few batteries.  You want 10 W out.  Let's say the boost converter will be 85% efficient, so that means it will require 10 W / 85% = 11.8 W in.  At 6 V from the batteries, that will be 2 A.  A few D cells aren't going to live long with that kind of drain.