Unfortunately, no, this won't work with the parts you've picked out.
Some of these conversions are supported - HDMI is backwards compatible with DVI, for instance. If you already had DVI out from your device, you could connect it to an HDMI port with a passive adapter (such as the one you've listed here). Passive adapters don't convert the video signal, they just take advantage of the fact that certain video output technologies were designed to be backwards compatible.
However, there isn't a "standard" passive DVI to Component adapter - the two technologies are largely incompatible. The one you've selected is intended for specific models of ATI Radeon cards that are capable of transmitting component video via the DVI port, but require an adapter and some special settings to do so. If you read the Amazon reviews, you can see a listing of the specific ATI cards it was designed for, along with some disappointed reviewers who tried and failed to do something similar to what you are doing currently.
If you must connect a component video source to an HDMI output device, you'll need what's called an "active" Component -> HDMI converter, for example this one. Typically these are devices that require external power, and they are capable of converting between video standards. However, these boxes can get costly, and the cheap ones tend to have significant signal loss or quality issues.