The CPUSA hasn't run a presidential candidate since 1980, IIRC.
Gus Hall ran in 1984.
the PSL is running a candidate but he's 28 and constitutionally ineligible to run for President so he didn't get ballot access anywhere.
Actually, the PSL is already on the ballot in
eight states (says seven in this link, but the PSL just got on in Iowa today). Some states require a stand-in presidential candidate if someone does not meet the "Constitutional requirements", so Gloria La Riva, the PSL's 2008 presidential candidate will appear on the ballot in those states. Keep in mind that when we vote in US presidential elections, we are voting for a slate of Electoral College voters not an actual presidential candidate, so Constitutional eligibility should not matter for who is printed on the ballot.