Where are you located? The laws are different depending on which country you're in.
Assuming you're in the USA, yes, there are laws that cover contests, competitions, sweepstakes, gaming, etc. Some are federal, some are state and some are local.
And, yes, the local laws may apply even for an online business. In fact, if you're going online, the issue is even bigger, because you may have to comply with the various laws in all
the areas you target for service.
Your best bet is to sit down for a consultation with a lawyer who can walk you through the regulations. You need to make sure that the structure of your contests is OK, that the rules are ironclad (the more money involved, the more likely it gets that one or more of the losers will sue, claiming some impropriety), and that the wording you use to describe your contests is allowable. (Yes, you can get in legal trouble just for using the "wrong" words -- referring to something as a sweepstakes when it really isn't, for instance.)
However much prize value you're looking at, you're also talking about potential liability in even greater amounts, not just from disgruntled customers but government regulators. You seriously do not
want to move ahead without consulting a lawyer.