When you install a second hard drive in a PC, it shouldn't get in the way of the original drive’s boot process. Of course, there’s often a big gap between what should happen and what does happen.
Let’s see if we can fix this problem.

Chances are that your PC is treating the new drive, which I assume has no operating system installed on it, as the boot drive.
Once upon a time, you had to check tiny jumpers on the drives to fix this. Now you just need to enter your PC’s Setup program (sometimes called the BIOS) and change the boot order.
I can’t tell you exactly how to do this, because it varies from one model to another. Generally, soon after you turn on the PC, well before Windows loads, a message similar to “Press F2 for Setup” flashes onscreen. Press whatever key it tells you to press.
This will bring you to the Setup program. Both drives should be listed on the opening screen. If not, there’s a hardware problem, which I’ll go into later.
Assuming the drives are both listed, it’s up to you to examine the menus, find the boot order, and change the drives. This can be tricky. You might find only one hard drive option in the boot priority list. In that case, there may be another option to select one drive over the other:

But what if one of the drives doesn’t show up at all? You may have loosened a cable when you installed the new drive.
Shut down the PC, unplug the power, and open the case. Check to make sure that no cables are loose. Remember that a hard drive needs two cables: SATA and power. If either of them is disconnected or loose, the BIOS won’t see the drive, and the computer won’t be able to use it.
What if the PC is truly bricked, and you can’t even get to the Setup program? Unplug both cables to the new drive and boot. If it boots fine with one drive and not with two, you’re probably overloading the power supply. Consider replacing it with something more powerful.
If you remove the new drive and it still won’t boot—even to Setup—I’d suspect that you damaged something else while installing the drive. At this point, I’d recommend taking it to a professional.