Possibly corrupt O/S after replacement of HD

I am out of my depth. (If my BSOD didn't work, I would never know, because I have no idea what it is. I am an old innocent.) The hard drive in my Acer Aspire laptop failed. The dealer installed a new one, and I then reinstalled everything from the DVDs of the system which I had made immediately after purchase, (using Windows system backup). I can no longer remember whether I had been making regular backups of the data, but think probably not. However, this crash prompted me to do so with appropriate care and diligence. The problem is that 1) the Windows backup will not run. (It drops me into the system32 directory when I try to set it up) 2) EasusToDo will not load, (gives a message that the installation files are corrupt) 3) Another program I tried, (forget the name) said it was missing a .cab file, and couldn't run 4) FileFort (from NCH software) ran for a day, but now says that it cannot find the F: drive, which is the thumb drive onto which I was backing up. (The F: drive shows normally in Windows Explorer, complete with all files.) It has been suggested that my O/S is corrupted. Does this sound reasonable? What is the best way to recover? (The install from the OEM DVDs is arguably corrupted, and one no longer gets a set of installation disks for the O/S as one used to.) I don't really want to go back to the OEM state, because it will require reinstallation of all the programs which have been installed since then, but if it would fix my problems will do so. But if it isn't going to get me any farther ahead than I am now, there is not much point.
The computer is an Acer Aspire, Win 7 Home Premium

As suggested try running Win7 System Image Recovery using the installer provided and burned to DVD or written flash stick with the tool given from Steps 1 and 2 in Clean Reinstall - Factory OEM Windows 7, booting into System Recovery Options.

If this fails you can order Recovery DIsks from Acer or follow the rest of the steps given to get a perfect Clean Reinstall which is a superior install to the bloated factory preinstall. Everything you need is in the blue link.

Far from an easy task, but I have blundered through it, with all your very kind help and direction. It looks as though all is now running as it should, and I am in the process of making a system image before adding back all the data files I saved prior to reinstalling Windows. And, to Zdruker, what I exactly was doing was trying to get the O/S fixed. The system image discs provided by the vendor when we bought the machine were corrupted. The original Windows installation on a second partition went south when the disc drive failed. When I restored the system onto the new drive from the original system image discs, I ended up with a corrupted install. And everything I did to try to fix it simply made things worse. You were all correct - the only way out was to start from scratch with a clean install of Windows. The various tutorials were absolutely invaluable. But I went awry at a couple of points: 1) I did not pick up initially on the fact that an iso file has to be burned with a specific program 2) I had significant difficulty with the drivers for the wireless connection. (They are not included in Windows). And, while one is instructed to "save the drivers" before wiping everything out, I never found out how one might possibly do so.

Clean Reinstall - Factory OEM Windows 7 specifically warns to put the wireless driver on a stick or CD to get online quickly to get drivers from optional Updates, and exactly where to find this driver. It's a shame you missed this since it is the only driver singled out in this way.

I don't know where you read to "save the drivers" but it is clear in the tutorial that they should come first from the installer, then optional Updates, then the Support Downloads webpage for your computer model or device.