1. First off, you cannot withdraw your intention to cancel your employment agreement. Effectively, all that happened is that your 24 hour notice period is just going to be replaced by a month notice period. The Basic Conditions of Employment Act state that if you have worked at a place for longer than a year, then you have to give four weeks notice. So, 28 days notice.
2. If, however, the contract is a fixed term agreement that ends on, for instance, 30 November 2015, there is no need to give notice. The contract ends on 30 November 2015 because the contract says so. Effectively, the parties has given each other 1 years' notice of the termination of the agreement when they entered into the agreement.
3. If the agreement ended on 31 October 2015, but you continued to be employed there, then the contract has been rolled on indefinitely and you would have to revert to four weeks notice as required by the act.
So, from the above, you should be able to tell if you are allowed to give 24 hour notice or not. If you are not allowed to give 24 hour notice, then we must look at what the consequences are going to be if you start at the new place tomorrow.
Your previous employer can sue you for damages due to breach of contract. But they can only get damages if they actually suffer damages. In other words, if your resignation results in them having to incur costs over and above your salary in order to replace you, then they would be able to claim that excess. If your leaving results in them losing a large contract with one of their clients because you are the key person and they were not able to ease the client into a transition, then they can claim that loss of income.
In most instances, however, where an employee gives 24 hour notice, there is very little to no damages, though.
I hope I have answered all of your questions and addressed all your concerns, but if you have follow up questions before you rate, feel free to ask them at no extra cost. If you are satisfied with the service, kindly rate it positively.