Yes you can use a usb stick, but it's a little more difficult to get the usb stick to boot. If you have access to another system running ubuntu, I'd suggest you download the lts desktop iso file, and then use ubuntu's startup disk creator to create a bootable live usb stick (I think it's called statrup disk creator - if you're running Unity, just search in the dash for it and it should come right up).
Once you've got the startup disk creator open, choose other file and point it towards the ubuntu iso you downloaded. You'll need sudo privileges to install the boot loader and persistence file onto the usb stick.
Once it's done, you'll have to press the key to enter your computer's setup (the BIOS) usually it is F1 or F2, just pay attention to it when it's booting. Repeatedly press that key when it's booting, and you'll get the BIOS screen. Once there, you'll want to look for boot priority and change it so that your usb stick will boot first (the usb stick will need to be in the usb port when you go into the BIOS screen or it won't give you that option usually). After that's done, save and exit out of bios, computer will reboot, and will read from usb stick.
Once ubuntu boots up, choose to run it live. Once the live desktop shows up, open a terminal and type sudo fdisk -l this will list all drives and partitions available on your computer and any attached storage (ie: the usb stick). You want to look for your harddrive (sda). More than likely you've only got one harddrive, so you will only see sda1 and possibly sda2 (the numbers after sda refer to partitions on that drive). If sda shows up, and you're sure that this is the drive your ubuntu installation is on, you will need to mount that drive/partition so that you can chroot into it. To do this, type sudo mkdir -p /mnt/ubuntu (this will create a directory called /mnt/ubuntu that you will use to mount to). Next, type sudo mount /dev/sda1 /mnt/ubuntu (this will mount /dev/sda1 to /mnt/ubuntu so that you can work with it). Next we need to chroot into the /mnt/ubuntu directory so we can work on your harddrive, so type sudo chroot /mnt/ubuntu Once you've done this, now our terminal is rooted to your harddrive (meaning any command we type into the terminal will be applied to your harddrive instead of the usb stick). So, now type sudo update-grub and grub will go through it's config process, and update the grub.cfg file on your harddrive. After this is done, you can get out of the terminal by typing exit until it closes. You can then shut down the live ubuntu session, reboot the computer, reset your BIOS to boot your harddrive first, and it should boot ok
If you are unfamiliar with all of this, I would suggest you take a little time and google all the commands I mention and get an understanding of them before you tackle this. Rest assured your files and folders are fine and completely unharmed. The only thing that's happening is that the boot loader is not configured properly to be able to boot ubuntu. Your actual harddrive and the data it contains is irrelevant to the problem you're experiencing. However, take your time, and understand what commands I'm referring to so that it stays this way. This might take you 1-3 days to understand all of this, but that's a small price to pay to make sure you don't lose any files on your harddrive accidentally.