I recently boiled some eggs, then put them in the fridge.  When I went to use them, they were not boiled all the way through.  Can I reboil them or should I throw them away?   
You absolutely can. I boiled some eggs last night. Ran them under cold water and put them in the fridge. Went to eat them today and they were too soft, like, whites still runny too soft. Stuck them back in boiling water for a few minutes today and then ran 'em under cold water again. They were perfect! Delicious, perfect texture, perfect. You can absolutely re-boil them! 