Also, at my new job, I could leave one rig on all the time, for free (at least to me..) it's a IT company, so having a computer running 24x7 at my desk is par for the course. Obviously not a huge setup but a normal looking pc system could churn away without a problem.
by saying that a computer running at your desk is something nobody would notice indicates that you are hoping to do this on the sly and not actually asking your employer's permission to do this. without their permission, you would be stealing their electricity.
I have limited funds, so I can't buy anything outright, but is there a way to lease some kind of mining rig?
one thing others have done is to offer to host (or host and operate) equipment for others in exchange for a portion of the proceeds.
back when people were hitting the point that they couldn't add capacity because the electrical circuits couldn't handle more or because too much heat was being generated, then colocating at another location was something that would be considered.
nowadays though anyone adding capacity is either going with fpga which consume just 10% of the electricity that mining the same amount via GPU does, or they are waiting on asic designs that are even more efficient.
so what you are offering isn't really of great value to anyone else anymore. and in four months, the block reward will be dropping in half so even if you were to acquire gpus today they wouldn't pay for themselves anytime soon. add in the damage should asic designs start shipping on schedule and you'll probably even regret getting involved in mining.
but there just might be some gpu mining operator that is paying the full rate and would be willing to colocate somewhere that the electric rate is much less. there have even been listings in craigslist looking for people whose electric is included in their lease and do a revenue share with them.