Date::Parse, Date::Calc, Date::Manip should be able to parse a date with varying degrees of limitations. Try also Date::ICal.

I have started to loath Time::Piece, which can also parse the date in OP's format, as it is limited to dates upto 2038-01-16T23:59:59. (That is the end point I could find with perl 5.8.7 built for i686-linux-thread-multi.)

Started to loath -- rant follows -- for it is currently used at my work where ...

1. it produced incorrect time zone on some of the machines (the offending part was replaced by POSIX::strftime);
2. in unrelated code not using Time::Piece itself, there was problem with dates in or after Jan 2038. Workaround was to set the limit to date in a year before 2038.

... given that above issues are known, I would rather be working on replacing Time::Piece usage instead of working with it.