HELP! car seems dead :/

[HellaSexyS13]

hello all.

so i live in nj and its been snowing and cold lately so i havent taken my s13 out at all, ive been starting like once a week tho and letting it run, but it always took at least two turns of the key to start and now i let it sit for about 2 weeks and went to start it today and there was nothing, sometimes when i turned the key i heard a bunch of clicks coming from the ecu i believe. i also tried to push start it and it barely sputtered. its an s14 sr20det by the way.

any ideas what these signs could mean, im almost sure the battery is dead but then im not sure why it wouldnt push start then...im stumped, any input would be greatly appreciated thanks.