I've done this job once before.

For starters, what new HDD are you using as the destination disk? Both WD and Seagate have available on their websites for free download customized versions of Acronis True Image. IF your new HDD is from one of them, get that software downloaded from the correct site. One significant limit is that each of these custom utility packages will only make a clone TO one of their units. For example, the Disk Wizard package from Seagate does not care what old HDD is the Source drive, but you can only clone TO a new Seagate HDD. Similarly for the Acronis True Image WD Edition from the other guys.

Another note for these and other cloning utilities. Many by default will propose to create on the new (Destination) drive a Partition the SAME SIZE as that on the old drive, and that usually leaves empty space Unallocated. If you read the manual file that comes with the software, you'll see that you can NOT accept the default settings and use the menu system to change to a different Partition size (like, the whole HDD) on the new drive.

Normally you might download the software onto your OLD HDD and install it there, then run it to make the clone. BUT if the old drive is unreliable, you may want to take different approach, as I did. I installed the software on the C: drive of a DIFFERENT machine, then temporarily installed both the old failing HDD and the new Destination HDD in that machine. Then I ran the software, making VERY SURE that is was set correctly as to which HDD units were the Source and Destination drives for the cloning operation. Don't forget that the DESTINATION unit will be wiped clean and everything on it replaced! So make SURE you have that set right!

When I ran my cloning operation this way, it started to tell me about Bad Sectors and asked what to do each time. After a few of these I got tired and used its menu choices to tell it to ignore all such problems and just keep on cloning until it finished. Yes, the software DID have such a handy choice available. Because of these errors it took a long time to clone an old 100 GB HDD, but it did the job. And here's the good news: so far the clone has worked perfectly! One might expect that Bad Sectors will mean that some of the files copied over will be corrupted, and if any of those are part of the OS, it might not work at all. However, in my case, apparently the Bad Sectors that did exist were not actually in use for any important file, and the clone copy works just fine!

By the way, I really recommend reading the manual file on such software. The customized Acronis versions I mentioned above do a LOT more that just cloning, so it's useful to learn what else they may help you with.