Depending on the nature of the fault of the hard drive, yes it is possible to recover files.
You can approach this two ways.
1) pay a data recovery company to attempt to recover the data for you - this can be quite pricey, but obviously some information especially baby photos are sentimental value and cant be repalced.
2) the old freezer bag trick. if you still have the HDD then you can try to recover the data yourself.
Do you know what type of HDD you had IDE or SATA ?
To recover the data yourself you need a means of connecting the HDD to your pc - I would suggest and external HDD dock (£20.00 approx)
I will give brief details, as there are several sites on google that will give you full detailed instructions.
It requires the HDD to be placed in a freezer bag along with a sachet of silica gel (the stuff that comes in shoe boes of in boxes of electrical gods) to absorb any moisture. Then seal the bag and place it inside another freezer bag. It is essential to make sure the bags are completely sealed.
Place the HDD in the freezer for at least 6-8 hours.
Once you had done this connect the drive to your PC and search for your files. Please note this is not guaranteed to work, and the HDD if it works at all will stop functioning again as soon as the temperature inside rises back towards normal operating temps.
I have managed it twice on old IDE drives and you only get a short period of time before the drive stops working again. However if all your photos are in one folder then it should be easy enough.