The computer I'm using is an Acer Aspire E5-575 with Windows 10. The page that should allow me to install isn't giving me an error message, nor doing anything else when I press the 'install' button. I have an added-on SSD drive that I was planning to install Photoshop to.
You have good news and bad news here. The SSD will be quicker than a regular hard drive. The bad news is, its silicon needs to be charged up or it won't retain data for more than a few days. If they last for 2 weeks you are lucky. This is a storage system that needs to be taken on vacation or when you get back all your data will go away. So it seems you may have the wrong drive to store Photoshop. AND, there's another problem: When you click install, your program is looking for the appropriate drive space to install the program. IF there is not a disc, it will not install. In respect to the drive you have, it's really a giant thumb-drive that needs to be charged up to run and keep charged to retain its data forever.
A good Seagate external drive is what experts use, and if its box says it has a 7200 rpm drive (or 8400 rpm drive) that's real external drive. But an external drive is not the place to install a program - because Windows is missing from this equation too. The REAL drive you need is the one in your computer. Install your computer on your drive C://. Installing it there will "root" Photoshop with Windows where it needs to be. Otherwise, if it's missing a real drive or Windows itself, it will not install. Windows is the platform which manages programs. This is also why there are no error messages. It doesn't have one for this.
External drives are plugged into the wall and doesn't need a charged, and its disc is magnetic and doesn't need a charge either. They are great for storing personal files (not programs) as your real program is your computer hard drive with Windows. An expert uses an external drive to store files, then unplugs the USB cable so the external drive doesn't get viruses, IF it should happen, then your files are safe. Experts also keep them plugged into the wall to keep them "warm" so they don't lose the data. As a software engineer, I know two brands of drives are out there, but the one I rely upon most is Seagate. Western Digital is another brand, has been reliable, but the cheaper priced models of this brand have a bad reputation. So I always go with Seagate.
I know you want a mobile drive but the key word is "mobile". The silicon drives which don't have a real rotating disc inside, are only mobile file movers which were made to move files from one computer to another in a jiffy. They need to be moved quick or they will lose data. On vacations, they need to be plugged into the USB as the USB gives them a power source because they don't plug into a wall. So the computer is its only source of power. Without it, data is lost quickly. And, if it's a cheap mass produced silicon drive l like your SSD drive, it will lose information even faster. This is the real reason, engineers don't rely on thumb-drives or SSD drives, and we WON"T especially use external drives marked "mobile". Silicon is new and exiting but useless in our World. But it's a good way for manufacturer's to make money on it! Use your hard drive from your computer to install the program. It's looking for a drive, drive space and Windows. It has .dll files to connect it to Windows. If any of those are missing, it will not install that program. As an engineer, I like to give the program install, and Windows advice.
Steve Lehman, MCSE
Windows uses something called UAC: User Authorization Control. It means that you must Ok the install before it will be allowed to begin. When you try to modify your PC by installing a program UAC displays a Window that requires a response. Sometimes the UAC window is not on top of other open windows. It is behind them and you might not see it. Look at the taskbar and if you see an icon that looks like a flashing shield or any flashing icon. Click that icon, it wants attention and until you respond to that the install will not continue.