Check your AutoPlay settings in control panel. I have AutoPlay disabled so any external media doesn't auto play. What you describe is the way my system works by default. I just go to the drive and run the setup or autorun file to launch the disk.
My Computer
At a glance
Windows 10 Education 64 bitAMD Phenom II X4 980 Black Edition Deneb 3.7GHz8GB 4GBx2 Kingston PC10600 DDR3 1333 MemoryZotac NVIDIA Geforce GT640 2 Gig DDR3 PCIe
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Home Built
OS
Windows 10 Education 64 bit
CPU
AMD Phenom II X4 980 Black Edition Deneb 3.7GHz
Motherboard
Asus M4N68T-M V2 µATX Motherboard
Memory
8GB 4GBx2 Kingston PC10600 DDR3 1333 Memory
Graphics Card(s)
Zotac NVIDIA Geforce GT640 2 Gig DDR3 PCIe
Sound Card
VIA VT1708s High Definition Audio 8-channel Onboard
Well if all else fails then another thing could be that there is something physically wrong with the drive =/ lets hope that it does not come to this but just another thing that could happen.
My Computer
At a glance
Windows 10 Pro x64Intel i7 477016GB 1600mhz DDR3Nvidia GTX 970 4GB
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Custom Build
OS
Windows 10 Pro x64
CPU
Intel i7 4770
Motherboard
MSI B85-G41
Memory
16GB 1600mhz DDR3
Graphics Card(s)
Nvidia GTX 970 4GB
Monitor(s) Displays
LG 29UM68 Black 29" ultra widescreen, and 27" ViewSonic