There are several potential issues. Most likely, a 10-year-old computer will not
have enough memory for a modern OS, the CPU is too slow for 1080P playback, the
video adapter is weak.

A DVR will be on most of the time. A computer such as the Acer Aspire Revo R3610
draws less power than your 10-year-old PC, enough to pay for itself in a couple
of years. It's no powerhouse, but it's OK as a DVR, and has a decent graphics
adapter.

I spent a few hours trying to shoehorn one of the tiny Linux distros into a 1997
PC. At some point I realized the computer doesn't have an ethernet adapter, so
it would be completely useless without spending some money on it.