Urgent help needed with OS install on new SSHD after XPS L702X OEM HDD failure

I'm a musician based in the UK and as an adjunct to my main studio DAW PC I've been using the family laptop, an XPS L702X, to run a cut down DAW to help organise things when I'm away recording in unfamiliar studios. I've got some recording time booked next week and the laptop has just suffered a terminal HDD failure. The error code details:

Error code 0142
MSG: error code 2000-0142
Hard Drive Test Unsuccessful Status: 79

Startup Repair
 
Windows cannot repair this computer automatically
 
Problem signature
 
Problem Event Name:    StartupRepairOffline
Problem Signature 01    6.1.7600.16385
Problem Signature 02    6.1.7600.16385
Problem Signature 03    unknown
Problem Signature 04    21200343
Problem Signature 05    AutoFailover
Problem Signature 06    4
Problem Signature 07    CorruptVolume
OS Version:                    6.1.7601.2.1.0.256.1
Locale ID:                       1033
 
I have a brand new Seagate SSHD ready to replace it with but here's where I started to hit problems. 
I originally wanted to use Acronis True Image 2014 to create a "Disk and Partition" image back-up of 
the drive (OS and Recovery) so that I wouldn't have to reinstall all my software let alone the OS. 
Unfortunately, every time I run it I get various iterations of the same error message:

Failed to read data from the disk.

Failed to read from sector '893,133,512' of hard disk '4'. Try to repeat the operation. 
If the error persists, check the disk using Check Disk Utility and create a backup of the disk. 
Failed to read the snapshot. (0x10C45A) CRC error. (0x100155)

As I've already tried fixing it and I know the HDD has died I guess this isn't too surprising. 
A friend suggested creating my own partition on the new SSHD and to use Acronis's File Back up 
function to create a .tib file of the OS and the Recovery files to copy over to the new drive using an Acronis 
Boot CD but suffice to say that didn't work.

So, I'm now at the point where I'm resigned to starting afresh - I've got an Inateck USB 3.0 to IDE+SATA 
Converter so I've plugged the corrupt OEM HDD into my PC to rescue all the important files I didn't want 
to lose so at least that's something. However, what I don't know is how I'd go about putting the Windows 7
OS onto this new SSHD. Stupidly I never created a backup using the Dell DataSafe software so is it even
possible to somehow use the Recovery partition to install the OS onto this new drive (I'm assuming that all
the OS info is stored in the Recovery partition?) or will it be a case of seeing if Dell can supply me with 
some discs to install the OS from (if they'll even do that?)?

If anyone could advise how best to proceed it would be very much appreciated as I have to admit that at this 
point I'm pretty flummoxed.

Many thanks,

Leigh.