The make of the disk doesn't really tell us how your data is being backed up onto that disk. Do you know what software it uses?
For example Time Machine copies files every hour in a way that is not bootable, but you can extract those files & get all your data back into a working OS.
Carbon Copy Cloner duplicates a disk in a way that is bootable - it would appear when holding alt at startup so you could use that to boot & inspect the state of the internal disk.
It may also be Seagate's own software that does something different.
Please try recovery mode, if that works you can try repairing the disk in Disk Utility.
OS X: About OS X Recovery - Apple Support
If that works, select Disk Utility & see if the internal disk can be repaired in the first aid tab.
Recovery mode can also download OS X & reinstall it, however you really need to know if the backup contains everything before that is attempted, otherwise you may lose data. The OS is also around 5GB so you may have issues if your internet is capped or unstable etc.
P.S.
I have no idea if this is helpful, but there may be help out there…?
http://belizeyp.com/Belize/I-T-Engineers-Consultants/profile
https://www.google.com/maps/place/VIP+wireless/@17.4938135,-88.1914518,4205m/dat a=!3m1!1e3!4m2!3m1!1s0x8f5c583ff12cb605:0x17a5a2f97fc838c3?hl=en
Search & ask around, you may find some help, try recovery mode first.