Ensure you supply the appropriate information on the Statement ending balance and Statement ending date fields, as these are essential for advancing to the next reconciliation process.
However, if everything appears to be in order but nothing happens when you click the Start reconciling button, I suggest logging out and then back in to QuickBooks to refresh the system. Alternatively, use a different browser and log in to QuickBooks to reconcile your account.
If this is your first time reconciling accounts, check out this article for useful tips: Fix issues when reconciling an account in QuickBooks.
Feel free to drop any other QuickBooks-related questions.