I am not sure what kind of methods you have found while searching the web but when I had to do something very similar a while back I found a very simple method that I still use up to this day when I have to change computers or format.
I would presume that you have something very similar to what I have setup on my computer since you said you have a external hd to store all your music. Something similar to the picture above but if now I left to 2 variations of my method to work with.
IMPORTANT SAFETY PRECAUTIONS: always copy your file never cut your file so in-case you screw up so you will have a backup to go back to. Never delete any file until you confirm everything is working correctly.
1. copy the itunes folder in your My Documents from your old computer. That should be located on ur C: drive or what you installed drive you installed itunes on. That itunes folder should not contain any music on it since your are using a external hard drive location. For people using the default location setup by itunes it will contain all your music files. This folder is very important because it contains all your itunes history, playlist and locations paths of songs on it. "red #1"
2A. take that copy and replace the new itunes folder that was created when you installed itunes on your new computer.
2B. for people not using a external drive to store music make sure when you install itunes back on the same drive letter now go back and do step 2A
people doing step 2B can skip step 3&4
NEXT PART VERY IMPORTANT
3. as you can see my all music files are all stored on my E: drive. "red #2" I am not sure what drive you have ur music files stored on it could be the D,E,F or etc but you have to make sure the path on your new computer is identical to old path on your old computer or it will not work.
4. plug in your external hard into your new computer make sure it is assigned the exact same drive letter it had in your old computer.
5. ur done, start up itunes and everything should be that way it was on your old computer.
GOOD LUCK
PS the reason "copy files to itunes media folder whening adding to library" is circled is because it keeps all the music stored in one place and makes the my method much easier to do.