The down side is that it all depends on how much the Drive has been used as to how effective and expensive the recovery is going to be. The First thing you MUST do is stop using the Drive Immediately and remove it from the system. If you do not have another computer to use you’ll need to replace the Drive in the computer with another HDD and load it with whatever OS you want and then depending on how important the Data on the Now Removed Drive actually is you can then decide how you want to proceed.
If the data is Important and must be recovered pack up the drive and ship it to your Data Recovery Specialist who can perform a Forensic Recovery and tell them what has happened. That is the cheapest and safest way to make sure that you recover as much data as possible at the least expense. At the extreme end of Forensic Recoveries it is possible to remove the Platters from the drive coat them in a special Goup and then fit them to a Specialist Machine and read everything that has ever been written to them on that machine. This however is very expensive and to my knowledge only ever used in Legal Actions by the Authorities. Real People and most business can not afford that type of Recovery and of course it destroys the HDD into the bargain as well, so you have to add the cost of a replacement HDD into the over all cost of the recovery and getting the computer working again.
However if it would just be Nice to recover the data and you can afford to loose it all you can try a Forensic Recovery Application and attempt the recovery yourself. It is however Important to realize that the more you mess with the drive unsuccessfully the less likely it is that any Professional Data Recovery Specialist will be able to recover your data so if you really must recover the data don’t mess with the drive as it’s only going to cost you more when you send it to the professionals and the less likely they will be able to recover all of your data. If you chose to attempt a Recovery you need to fit the drive to a system where it can be read from but under no circumstances do you ever write anything to the drive you just read it and save any recovered files to another HDD or something else depending on what you have available.