Depending on the language of the email you received, you may or may not have a valid claim to initiate a legal action. Based on the wording, the email may constitute an offer which, through your acceptance by email itself (and not necessarily signing the agreement), a valid contract may have been executed thus giving you a right to take legal action, although, the terms of the contract would then have to be scrutinized. The wording of the email may also be interpreted in a way such that only upon the execution of the agreement by BOTH parties will the employment contract be formed. Assuming the latter to be true, if the startup hasn’t executed the contract, I’m afraid you may not have recourse under contract law.
In relation to the compensation, the language of the email exchange and any documents would determine if they can be held liable for paying such an amount to you or not.
You can get in touch if you need clarity on this issue.
Firstly, did the employer send you a signed copy of the Agreement. If not, by only signing the Agreement, it would not amount to an executed Agreement. Secondly, please check the 'Term' clause of the Agreement - whether there is any provision with respect to 'Probation'. If yes, does it give a right to the employer to terminate the employment without giving any reason or notice during such probation period.
As it was a contractual engagement, what is provided in the Agreement would be pertinent to analyse the situation.