There are more electronic judges systems for holding competitions. One famous enough among competitive programmers is "ejudge".
However, perhaps it is not necessary to cling to "standard" format of competitions with submitting code and running it on server.
Facebook Hackercup used checking by answers at least at first round(s). Tasks could be designed to be less or more suitable for such an approach.
I even dare to say that I can propose holding competition in such format at my website - currently here is enough infrastructure. We can only develop some problems with persons who are chosen to be problemsetters and I'll add them into separate volume.
Well... and we need to agree on winning criteria. I suppose that competition should be run for several days, not for 1 or 2 hours at some specific time - this will allow to participate independently of timezone.
I'm not sure it is the best idea, if implemented so straightforward.
People involved in competitive programming will easily solve all such "directly algorithm-based tasks".
Instead we can hold a kind of programming quest... The first task somehow hints the clue for second with its solution, second gives a codephrase for third etc.
BTW: If we could not afford offering sufficient money prizes, perhaps it would be better to propose T-shirts as prizes? Of course it requires producing them and sending but if for small number of T-shirts it is not that hard.