ok, let me get this straight.
You are connecting to the Synology from your desktop PC, when you change the IP address of the Synology to a static IP address you cant connect to it but when you allow it to pick up the IP via DHCP you can?
When you say you can connect to the "Server" remotely are you referring to the mobile app / synology account? The reason I ask is you have not mentioned anything about changing the Firewall rules on your firewall / router which is purely because the device is authenticated and or using UPNP.
After changing the Device IP address can you browse to its web front end using https or http?
If I have this the wrong way around let me know, just trying to get an understanding as changing the IP on the synology and trying to access a share on it using \\192.168.0.136 may not work until the NIC is took down and brought up again, the web server runs independently to the SMB / CIFS mount points so it could just need refreshing.
Again if I have this the wrong way around let me know