RichardEL is probably correct. I’ll go through your questions.
> there is no Mac OS partition, I assume it would be directly underneath the HD on the left?
I have not seen this particular condition where the hardware disk icon appears but the system volume that is supposed to be below it does not. The System Disk partition would be below the HD icon indented to the right. It is usually called “Macintosh HD” unless you renamed it.
> when I go into disk utility my HD appears on the left, but I can repair or verify it
Odd. It appears but you cannot manipulate it with Disk Utility.
> The S.M.A.R.T status reads verified
If it did not say Verified then it would indicate a problem. Saying Verified does not rule out problems but I think it indicates it is still breathing.
> Is the HD deceased?
If you booted the Recovery Partition (Boot, Command-R), which it sounds like you did, then at least part of the disk is still breathing. If it took a long time to boot then that may have been a Network Recovery boot which would indicate the disk is very sick or dead.
> [If I] restore from time machine [will] everything will be back as it was before?
Yes. That is the beauty of Time Machine. All your data, applications, and system preferences will be as they were as of the last backup.
> I was thinking of erasing the HD, would this be of any help or do I just need a new one?
Given what you reported from the Disk Utility steps you took it is unclear to me if there will be a way to repair the current volume, if you can erase and install from scratch or if you need a new disk. Before proceeding it may be useful to have an expert at an Apple store look at it for you. They may be able to revive it without a clean install or new disk.
As was the case above, it could be a good disk with a bad cable in which case a new disk is not going to help. To test this you can purchase an inexpensive external enclosure, remove the internal disk, place it in the enclosure, plug it in and then use Boot-Option to attempt to boot from the now external disk. Here are links to the screwdrivers and enclosure you would need.
$5 Toolkit: http://eshop.macsales.com/item/OWC/TOOLKITMHD/
$22 USB 3.0 enclosure: http://eshop.macsales.com/item/OWC/ES2.5BU3W/
If you attempt a clean install, use the Partition tab to repartition the disk, selecting one partition and with “Options…” electing a GUID partition. Then use the Erase tab, select “Security Options…” and set it to write a single pass of zeros. This will write to every sector to map out bad blocks. (If you have an SSD do not write a pass of zeros.)
If you do need to replace it I recommend an new inexpensive (~$100) and super-fast hybrid SSHD drive that has an 8 GB SSD cache that makes the data fly. Google “Seagate 1 TB hybrid SSHD”.