I set up an HTPC to record shows that come on during hours in which I am away from the TV so that I can watch them at my leisure.

Just last week, the CPU fried and my HTPC is dead.

Is it infringement for me to the go to the pirate bay and download the very episodes I recorded, legally, so that I can still watch them?

I have an HTPC too. Great stuff. But to answer your question, yes, it’s infringement.

Why?

Remembering of course that it is prima facie infringement to record directly from a broadcast to which one is legally authorized to view (whether by right, as in the case of over-the-air broadcasts, or by private agreement, as in the case of subscription cable and satellite), but that this could be fair use if for the purposes of time shifting. To help out, here’s the relevant bit of the Betamax opinion:

[T]he District Court’s findings plainly establish that time-shifting for private home use must be characterized as a noncommercial, nonprofit activity. Moreover, when one considers the nature of a televised copyrighted audiovisual work, see 17 U.S.C. ? 107(2) (1982 ed.), and that time-shifting merely enables a viewer to see such a work which he had been invited to witness in its entirety free of charge, the fact that
Page 464 U. S. 450
the entire work is reproduced, see ? 107(3), does not have its ordinary effect of militating against a finding of fair use. [Footnote 33]
This is not, however, the end of the inquiry, because Congress has also directed us to consider “the effect of the use upon the potential market for or value of the copyrighted work.” ? 107(4). The purpose of copyright is to create incentives for creative effort. Even copying for noncommercial purposes may impair the copyright holder’s ability to obtain the rewards that Congress intended him to have. But a use that has no demonstrable effect upon the potential market for, or the value of, the copyrighted work need not be prohibited in order to protect the author’s incentive to create. The prohibition of such noncommercial uses would
Page 464 U. S. 451
merely inhibit access to ideas without any countervailing benefit. [Footnote 34]
Thus, although every commercial use of copyrighted material is presumptively an unfair exploitation of the monopoly privilege that belongs to the owner of the copyright, noncommercial uses are a different matter. A challenge to a noncommercial use of a copyrighted work requires proof either that the particular use is harmful or that, if it should become widespread, it would adversely affect the potential market for the copyrighted work. Actual present harm need not be shown; such a requirement would leave the copyright holder with no defense against predictable damage. Nor is it necessary to show with certainty that future harm will result. What is necessary is a showing by a preponderance of the evidence that some meaningful likelihood of future harm exists. If the intended use is for commercial gain, that likelihood may be presumed. But if it is for a noncommercial purpose, the likelihood must be demonstrated.

In this case, respondents failed to carry their burden with regard to home time-shifting. The District Court described respondents’ evidence as follows:
“Plaintiffs’ experts admitted at several points in the trial that the time-shifting without librarying would result in ‘not a great deal of harm.’ Plaintiffs’ greatest concern about time-shifting is with ‘a point of important philosophy that transcends even commercial judgment.’ They fear that, with any Betamax usage, ‘invisible boundaries’ are passed: ‘the copyright owner has lost control over his program.'”
480 F.Supp. at 467.
Page 464 U. S. 452
Later in its opinion, the District Court observed:
“Most of plaintiffs’ predictions of harm hinge on speculation about audience viewing patterns and ratings, a measurement system which Sidney Sheinberg, MCA’s president, calls a ‘black art’ because of the significant level of imprecision involved in the calculations.”
Id. at 469. [Footnote 35]
There was no need for the District Court to say much about past harm. “Plaintiffs have admitted that no actual harm to their copyrights has occurred to date.” Id. at 451.
On the question of potential future harm from time-shifting, the District Court offered a more detailed analysis of the evidence. It rejected respondents’
“fear that persons ‘watching’ the original telecast of a program will not be measured in the live audience, and the ratings and revenues will decrease”
by observing that current measurement technology allows the Betamax audience to be reflected. Id. at 466. [Footnote 36] It rejected respondents’ prediction “that live television
Page 464 U. S. 453
or movie audiences will decrease as more people watch Betamax tapes as an alternative,” with the observation that “[t]here is no factual basis for [the underlying] assumption.” Ibid. [Footnote 37] It rejected respondents’ “fear that time-shifting will reduce audiences for telecast reruns,” and concluded instead that “given current market practices, this should aid plaintiffs, rather than harm them.” Ibid. [Footnote 38] And it declared that respondents’ suggestion that “theater or film rental exhibition of a program will suffer because of time-shift recording of that program” “lacks merit.” Id. at 467. [Footnote 39]
Page 464 U. S. 454
After completing that review, the District Court restated its overall conclusion several times, in several different ways. “Harm from time-shifting is speculative and, at best, minimal.” Ibid.
“The audience benefits from the time-shifting capability have already been discussed. It is not implausible that benefits could also accrue to plaintiffs, broadcasters, and advertisers, as the Betamax makes it possible for more persons to view their broadcasts.”
Ibid. “No likelihood of harm was shown at trial, and plaintiffs admitted that there had been no actual harm to date.” Id. at 468-469.
“Testimony at trial suggested that Betamax may require adjustments in marketing strategy, but it did not establish even a likelihood of harm.”
Id. at 469.