If you want to compel your tenant to pay rent and/or leave the space, you need to file an eviction proceeding as soon as possible. Since the lease is over and your tenant has not paid July rent, you can begin a holdover proceeding immediately. Keep in mind, though, that if the tenant tenders rent for July and you either accept it or even delay substantially in returning it to the tenant, you will have converted the expired leasehold into a month-to-month tenancy, meaning that before you can commence a holdover proceeding, you will have to serve a 30-day notice of termination, running from the next day that the rent would be due. Here, for instance, if you were to accept rent on 7/9/2012 and then serve a 30-day notice of termination of the lease on 7/10/2012, the 30-day notice would have to state that the lease is terminated effective 8/31/2012, which is 30 days from the next day that the rent would be due (8/1/2012), assuming that rent was paid on the 1st of each month under the original lease agreement. A 30-day notice served on 7/10/2012 that purports to terminate the lease effective 8/10/2012 is invalid and will result in having to start the process all over again. There are many other technical requirements under Article 7 of the Real Property Actions & Proceedings Law (governing summary eviction proceedings), many of which are equally capable of defeating an eviction if you're not careful to comply with them.
As for the broken glass, I suggest fixing it and adding it the charges of unpaid rent. You are entitled to enter to make emergency repairs, and I think this would qualify due to the safety issues involved with a broken window (though I would always try to get the tenant's permission to enter first).
I strongly recommend that you retain a landlord-tenant attorney to handle the eviction. It's not easy to accomplish an eviction, even with counsel, and without an attorney you are setting yourself for a long period of time without possession or rental income because of all the hyper-technical, counter-intuitive procedural requirements. Plus, most non-attorneys are not experienced in negotiating legally binding settlements, cross-examining witnesses, or doing any of the many other skills potentially needed to obtain an eviction. And, if your building is owned through an entity such an LLC or corporation, the building cannot send you to appear in court -- you must retain a lawyer to appear on behalf of the company. An attorney can help make sure that the process goes as quickly as possible, and may be able to help you negotiate an agreement for the tenant to leave quickly in exchange for relief from the full balance owed. It sounds like this tenant is not interested in negotiating at this point, but when he is facing an eviction and entry of a money judgment against him, he might feel differently.
Best of luck in regaining possession and getting paid.