I think it is possible to build a very capable HTPC for under $200, but OP would have to be creative.
I am writing this on a $100 Desktop that has:
AMD Athlon II X4: $50
ECS motherboard: $10 After rebate
ATI Radeon 5400 Video card: $10 After rebate
8 GB (2x4GB) of DDR2 RAM: $20 After rebate
Windows 7 copy: $10 at University store (don't ask me, I can't buy you one, but if you or someone you know is a student or employee at a major university, then you can get your own copy for $10, download, no physical disk)
Microsoft Office 2010: FREE at university store (download, no physical disk)
Case: Used an old case
PSU: Came with the used case.
Keyboard/mouse: $10 for combo.
Someone with a much bigger budget (200% of mine) can do lots more.
6 TV's in the house on FiOS and we only pay $4.99/month to connect them all!!! Power to the CableCard and WMC7!!!