In a "copy everything" manual operation, it is always possible to miss something, especially if some software has placed hidden files on the original. An even easier and sure-to-work process is cloning. You need a software utility for this and you can buy some; there may also be freeware software for this.
IF you buy your new HDD from Seagate, you can download from their website for free a package called "Disk Wizard" that, among other things, can make a perfect clone of your old drive to a new SEAGATE drive. OR, if you buy from WD, go to their website for a package called Acronis True Image WD Edition, which will happily make a clone to a WD new drive. As it happens, both of these are customized versions of Acronis True Image, a VERY good package that does LOTS beyond cloning, so be sure to get the manual and read it! Other HDD makers may also have free cloning utilities for their units.
To use either of these you must have the old and new drives both connected up and be able to boot into Windows. (With a brand new HDD you will NOT see it in My Computer because it has not been Partitioned and Formatted. Do NOT worry about this - the cloning operations will do those jobs for you.) You must install the utility on your machine - in your case, probably on your old D: drive. Then you start the utility and find the menu portion for making a clone The very FIRST thing you must do carefully is specify the SOURCE unit - your old D: drive - and the DESTINATION unit - your new drive. Get the DESTINATION right - it will be overwritten.
Now you will need to adjust some settings - some will need to be changed from defaults. First is the size - often the default will offer to make a Partition on the new HDD the same size as the old drive, but you want it to be much bigger - the whole drive space. So you just change that. You do NOT need this clone to be bootable - you use your other C: drive for that, and this new one will contain only data. For a File System it will suggest NTFS and that is right. You can let it do a Quick Format which does the essentials in 10 to 15 minutes before starting the cloning. OR you can do a Full Format which takes MANY extra hours to test the whole HDD before using it, but I usually do not do this for a brand new disk. Your choice. When all options are set your way, run the task. It will take a fair amount of time to copy a full 500 GB drive.
When it is finished, shut down and disconnect the power. Go into the case and disconnect the power and data ribbons from the new drive. Now disconnect power and data ribbons from your old one, and connect them instead to the new one. Keep your old drive disconnected. Close up, connect power and boot up. Your D: drive should have a whole bunch of empty space and everything else should be working exactly as it always did.
Shut down, power cord off, and open the case. Now connect the spare power and data ribbons to your old drive again, close up, power cord on, boot up. The old drive should show up as a drive with a new letter like "F:" or something. All its files will still be on it, but it has a new name. You can Format it to completely empty it off and start using it as another data holder. If you do, I'd run a Full Format to check it. Or you might consider removing it and installing in an external enclosure to become a portable HDD or a backup unit.