Firstly Congratulations on switching and welcome
2nd This is posted out of place there is a board specifically for mac osx related questions (you'd prob get more responses by starting a new thread there)
and finally I can answer your question!!!
Your PC is probably not responding with the external hdd because of the way it is formatted. I'm thinking a mac only format is applied to the drive making it inaccessible to the PC. If you simply use Disk Utility (use command + spacebar to activate spotlight and type disk utility) you can use that which has a list of formatting options and descriptions as to what type of machine the partition is readable for. Unfortunately this means your time machine backup will be erased along with formatting. If you plan to use the drive exclusively with a mac then I recommend formating with windows (NTSC) and then transfering your files. After that reformat again in OSX with the mac only partition and do another time machine backup.
Congrats again enjoy your new