Can you access the Eve Online test servers with a trial account?

In order to access the Singularity server you need to have an active account on Tranquility. The account needs to have been active at the time when the current mirror was taken, this date is usually mentioned in the Test Server Feedback forum.

For example, if your account expired on August 15th and the database mirror is taken 3 days later, your account will be inactive on Singularity, even if you reactivate it on Tranquility afterwards.

If your account is active on Tranquility but you find you are having login problems on Singularity, you can look for help in this forum-thread.

Kelly Williams: http://wiki.eveonline.com/en/wiki/Singularity

Eve Online Trial

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Finally, that's what I was exploring for! Thanks to author of this question.