sd-dvr40 as web server

Well, I suppose it's possible. "Hack" the box and install TiVoWebPlus on it. It will then serve HTML pages for you. You'll be limited to one connection at a time, I think. What sort of things do you want to serve that you think this will work for?

You're Tivo has a 200+ MHz CPU and 48 MB of RAM - I wouldn't expect it to be a very good server.

I doubt it has the normal other support chips that are in a PC to allow it to even run DOS.

And we won't even think about the keyboard, mouse and monitor.

A web server doesn't need a keyboard, mouse or monitor. Most commercial web servers have none of those. But indeed the TiVo is quite underpowered for web server purposes and the server is a TCL script further hurting performance. Whether or not this matters depends on what you want to use it for.

But, don't you need some kind of peripheral to at least load server software? I ask rhetorically. Okay, put the HD in a PC and load it that way.
I possibly took the OP question too broadly.

No - as I mentioned above, you can load TiVoWebPlus which is a simple web server. It will respond to http requests on port 80 and serve up files. Yes, at some point, to hack the TiVo, you have to pull the disk and stick it in a PC, but once that is done no other peripherals are needed.

As long as you can get an OS running to the point that you can FTP and telnet to it (or even serial bash), you can go from there and install a binary compatible web-server app, or appropriate compilers and compile source code.

And before all that, write a kernel to use full drive EXT3 and format it as such.

All said, it will be better to not think of it, but use a PC or purpose built appliance for a web server.

Buy a Pentium II or whatever at a garage/yard sale for $5. It would make a much better web server.