I need to start up an EC2 instance at (say) 6am every day. The constraints are that I\'d like to avoid having a computer running all day to do the startup or use a paid solu
Given your constraints, the desired functionality is unfortunately not covered by the two dedicated automation mechanisms available as AWS Products & Services right now:
While starting/stopping/rebooting an instance conceptually falls into the manage category of the latter, it is not available like so (which incidentally is the reason we provide a separate Task specifically for this functionality within the meanwhile deprecated Bamboo AWS Plugin and its successor Tasks For AWS).
Consequently the approaches outlined in my answer to How to turn on/off cloud instances during office hours are still applicable, albeit with the additional constraint that you would need to find a provider hosting your script or continuous integration solution for free:
Hosting scripts has e.g. been possible for quite a while already by means of those cron job providers.
Given the current explosion in Platform as a Service (PaaS) solutions there are quite some providers, that will allow you to do host scripts and/or continuous integration solutions one way or another as well.
Obviously you'll need to verify, whether using the free tiers available for purposes like this is acceptable according to the respective Terms of Use of a provider in question.