Hello Brad - You're doing good so far, it's better to take your time than rush through this. We're getting to the point where it's time to prioritize things, so we'll deal with the most important things first. Being able to boot from either the Toshiba external drive or the USB stick is vital to the whole plan. When you go into the BIOS settings, look for a page or a section for "Boot Options" or "Boot Configuration". In that section, you should see a way to access "Boot Order", or a subsection listed on the page itself. It should look similar to this:
Boot Order:
Hard Drive
Internal CD/DVD ROM Drive
USB Diskette on Key/USB Hard Disk
USB CD/DVD ROM Drive
Network Device
At the top or bottom of the page, there should be a bar explaining what the "F" or function keys are used for. Whenever I use the word USUALLY in this example, be aware that I'm talking about the Function Keys used in my BIOS, not in yours. Yours could be different. Read and understand what your function keys are used for, do not take my word for it.
All you want to do here is change the boot order, nothing else. USUALLY the F5 and F6 keys move an item up or down in the boot order, you may have to select or highlight the item first, using the page up/page down keys . When you get that item to the top, USUALLY F10 is used to save the settings and to exit BIOS. You may have to try using USB Hard Disk for the Toshiba and USB CD/DVD ROM for the USB stick, it will depend how your BIOS "sees" the hardware. Try different combinations, you may find that one setting will work for both. I can't really offer more in the way of advice on this, you'll have to experiment and be careful with what you're doing. USUALLY the F9 key will reset everything to the default settings if you think you messed things up.
Next, Ken W's idea of using the CHKDSK /R command is good, it could recover any data in the bad sectors. Be aware that it will take a long time to run, it's up to you if you want to use it. The reason it didn't work for you is you have to right click the command prompt and select "Run as Administrator" to use CHKDSK. Use all capitals, and enter "CHKDSK C: /R" (without the quotes) for the C: partition and "CHKDSK D: /R" for D: partition. Also note there's a space between the colon and / mark.
You did the right thing saving all your files from D: to your own Toshiba, it's almost enough to fill the entire drive. If you shrink C: partition down a little more, so that it's 280GB (286720MB), you'll be able to save both the recovery partition and C: partition to your dad's Toshiba, and have a little room to spare. Did you get a chance to read the link I posted and watch the video? If you can drag and drop files, it's basically the same. Click on the recovery partition first, select "Clone this Disk", then move the recovery partition to the target drive, keeping it at the front of the drive. Then move the C: partition. Hit "Next" on the bottom of the page, read the summary on the next page to see if it looks right, then hit "Finish". Remember, you can do this over if you have to. Go back to my previous post to read how to boot the Toshiba. You can use it until you get a new drive. When you get your new drive, clone these two partitions from the Toshiba onto it, extend C: drive to where you think it's right, create and format a new D: partition (use NTFS), then copy the files to D: from the other Toshiba, and you're back in business.
And last, plan B, the safety net. By downloading the ISO file, and using Rufus to create a bootable USB stick, you will have a way to do a fresh install of Windows 7 to your new hard drive, just in case something goes wrong with plan A. It's the same as having the installation DVD, I chose this because you mentioned you weren't too thrilled about buying Windows 7 again. As long as you have a valid activation key, you'll be fine. Keep in mind, you only want to test this to be sure it will boot. DO NOT select to start the installation, or it will start to overwrite either the hard drive or the Toshiba. Kill it on the first screen by clicking the red x in the top right corner, the same way you would close a program. To be absolutely safe, make sure to do the clone to the Toshiba first, and make sure it boots, then be sure to disconnect it, before you try testing the USB stick.
All right Brad, I think you have everything you need to do this. If you're unsure about something, or if you run into problems, post back, we'll take it from there.