The form factor of a SSD is obviously different than that of a 3.5" HDD. You need a special adapter (not the one above) because your Z600 has the HP "drawer" type of drive holder that slides in and the drive connectors slip in to a "BlindMate" connector made by Foxconn that is centered to the left rather than more to the middle as many adapters place the SSD. The one referenced to by the post above will work great for a xw workstation that has cables to the drive.... but the Z600 and Z620 etc that use the drive drawers need special attention.
So, search this forum for Blindmate. An adapter that works well is the Western Digital IcePack.... check on eBay. The newer versions have the fins going the short way, not the long way.
One of my favorites is made by Foxconn for HP, and is reasonably priced on eBay: Search there for 654540-001 and expect to spend less but wait longer for one from China (where they are made for HP). You can see what a BlindMate connector looks like when you search those.
This all has been posted about here in the forum so look in here for IcePack and 654540-001 too.
For drive issues..... If I hit a snag I always pull out my bootable CD of DBAN, boot from it, and do a low level format of the drive. DBAN is free... the one that gives you a certificate and the one that does not are identical, and you download the .iso and burn the CD from that. Be careful to always know what you are targeting.... it is a full very low level reformat down to clear out all boot sectors. It takes time... let it run over night. Then, use MS Manage Disk Management to create a new MBR partition, and then do a long type of NTFS format from Disk Management. That is, uncheck Quick if that happens to be checked as you go through the process. If that does not work then you likely have a bad drive.