It does share compoents. The transform is DCT-like. The fact that it is 4x4 and integer is irrelevent. The basic structure is the same. People have been implementing integer multipy-less DCT implementations for years. The fundamental transform is DCT-like and is implemented the way all such transforms are (DCT, FHT, FFT, DWT, etc) via a "butterfly" structure. If you've got flexible hardware to compute transforms, than reprogramming it to use the H.264 transform is a matter of changing coefficients and kernel size. For example, in TI's OMAP processors in cell phones, they cover an entire range of compression codecs by making their kernels and butterflys adjustable. If you're got totally fixed function hardware, you may be screwed, unless you look at academic work on transcoding which developed transforms between MPEG-2 DCT and H.264's 4x4 DCT. But I think it is a bit disingenous to say that there is nothing shared. H.264 is not a revolutionary new codec, is an extension of existing techniques.
For motion comp, it depends if your HW's kernels are programmable or not. In NVidia's case for example, the DCT and motion comp are supposed to be done via programmable built in combo scalar/vector/branch unit.
Other parts, such as deblocking, conversion, deinterlacing, are also reused. And quantization (inverse) seems to be done by the CPU for most systems today.