You have already done a fair bit of troubleshooting, so we know its not a local issue with your WIFI by you already trying on the train, verified WIFI is enabled on the tablet, and can confirm the WIFI is working as your phone connects. This sounds most likely like a software fault in the tablet itself.
With regard to SSID some WIFI's are setup as hidden, so they dont broadcast their name (SSID) and not discovered by a WIFI, the only way to connect to these WIFI' is to know their SSID, but since you know they should appear in the scan as they show up on your phone I wouldn't concern yourself about the SSId.
With issues such as this the most effective approach is to perform a factory reset, before do so I recommend you ensure all the files are back up using the Samsung backup facilities as documented on page 137 of the manual here.
In essence go to Settings > General > Backup and Reset, ensure Backup My Data is enabled.
To perform the factory reset as detailed on page 128 of the same manual; in the Backup and Reset menu select the option Factory Data Reset, acknowledge the warning advise personal settings will be lost.
The Tablet will then restart after a while, and present you with a wizard asking you to enter in your google account credentials, at which point you will then be given an option to restore you device.
Check the WIFI wizard is now able to scan and find WIFI services.
Do you still require assistance, I haven't heard from you in the last few days?
This would suggest there is a fundamental hardware fault on the tablet, a factory reset hasnt resolved it which rules out a software issue.
As such I am afraid the product is uneconomical to repair, as the main board where the wifi chip is housed is near enough the same price as the cost of a new tablet.
Depending on what your using the tablet for, I happen to know there is a cheap Android tablet going for £50 which is a similar spec to your Samsung one (I found for another customer), it can be purchased here.
Please let me know if I can be of any further assistance, otherwise I would appreciate it if you can rate the service received.