Reply #1: He did in the 1984.. He lost the Democrat primaries.

[Eric J in MN]

from wikipedia:

Glenn also mounted a bid to be the 1984 Democratic Presidential candidate. Early on, Glenn polled well, coming in a strong second to Mondale. It was also surmised that he would be aided by the almost-simultaneous release of The Right Stuff , a movie about the original seven Mercury astronauts in which it was generally agreed that Glenn's character was portrayed in a pleasing and appealing manner. However, Glenn apparently turned his attention to national politics too early, neglecting the sensitive voters of the Iowa caucuses. Media attention turned to Mondale, Gary Hart, and Jesse Jackson, leaving Glenn the strongest also-ran. The 1984 presidential bid left Glenn with a substantial campaign debt that took years to pay off.