If you have extract ingredient kits, go ahead and start the brew. The kits I've seen already tell you what the OG will be and they are quite accurate if you follow the instructions. I may get jumped on for saying it, but I've found that if you follow their instructions for brewing and are just a bit patient, you don't have to use the hydrometer at all. The patient part is waiting until you can be reasonably certain that the fermentation is complete, like 2 1/2 to 3 weeks or even more if you are brewing a porter or stout. It would be nice to take a final gravity reading if you can.
Midwest has a good reputation for replacing missing parts of kits and I suspect they might for parts broken in shipment too. The only time I emailed, I had an answer within a day or 2.