I'll try to address each of these points, AD.
Assume that I have ~$10,000 to spend on equipment to start a home-based business that involves creating short custom video.
You can do a lot with 10 large. I think you can do everything you want (except as noted below) with about half that (for equipment).
1) Capture 10-15 minutes of video and still images including sound at the highest quality possible (in a static, high-light, interior environment)
When you say "at the highest quality possible" I'll assume you don't mean Digital HD, which would cost about $25,000 for just the camera.
You can get a REALLY GOOD DV Camcorder with pro features for under $1,000 now.
2) Be capable of editing the video, adding music, text, voiceovers
I like Avid Express for quick video editing, but Slink has far more experience with this than I do. Please also note that I believe he and I are mostly Windows users. There are other options for a Mac if you want to go that way.
3) Be able to produce DVDs that would be difficult to duplicate or extract files from
I don't think this is possible given the current DVD technology. The problem is that I assume you'd want these DVDs to play on stand-alone players as well as PCs? If so, you're limited to the copy protection and security that DVD players offer. Which is to say: none.
I'm not sure why this would be an issue - you don't want clients being able to make their own copies?
There hasn't been a copy protection scheme yet that hasn't been broken. I would recommend you LET THIS ONE GO for your own peace of mind. You'll also save yourself a lot of expense if you don't chase the dream of trying to make something uncopyable. Usually you'll just make it totally unplayable and piss off the people you're hoping will give you money.
4) Store the complete files in physical or electronic format for future reference, including potential updates or for re-ordering of DVDs
You could store the DVDs on a series of large hard drives, but of course you could also just keep a copy of the DVDs (offsite) for this purpose. Just make sure you keep more than one copy in case one of the discs goes bad.
5) Be able to create the DVDs in formats readable overseas, particularly Japan and the Phillippines
Keep in mind that there are two major video standards for TeeVees - NTSC (North America and Japan, and Some of Korea) and PAL (everywhere else).
So Japan and the Phillipines use different video standards. But if you keep video masters you can make different DVDs for different regions using the same source files. It's just a matter of encoding.
Also, the whole "region coding" thing is optional - if you're authoring your own discs you can set them to region 0, which is playable everywhere (alternately, you could region encode them to a specific region, but this is again easily defeatable).
6) This enterprise in no way involves depiction of sexual activity or unclad people of any age, gender or persuasion.
Then what good is it?

Without knowing what you're wanting to do it's hard to say what you should do, but generally to edit videos and create DVDs (I'll assume you're doing one and two offs, and not wanting to have thousands pressed - if so, you'll want to quadrupal your budget).
A high-end PC, preferably with at least 4Gb main memory, two 3Ghz hyperthreaded processors, a few 300Gb hard drives, DVD burner(s), etc.
I'm going to say you can get that for $3,000.
Video editing software: $500-$1000
Digital Video Camera (w/ firewire interface): $1000
Extra HD Storage (Firewire or USB2): $300 each per 300Gb (I recommend Maxtor's OneTouch drives - they're stackable and are quiet, cool (temp-wise), and reliable) - figure two or three of these to start - easily added onto later.
So for equipment alone figure around $5,000 max, and that's only if you want dream equipment that will make your job a happy one.