While installing my new waterpump, I threaded one of the bolts a little too tight and snapped it off. The bolt broke at a point just inside the engine block. it is impossible to remove that part of it by normal means. What do I do?

That really sucks! Been there, done that. You probably will need to drill the center of the bolt and use an "easyout" to back the bolt out. However access is probably very tight. You may be better off cutting your losses now and taking it to a professional. In my case, I broke an easyout bit off inside the broken bolt, before taking to a professional. He wasn't too happy about having to drill out the hardened steel easy out, but he got the job done...