First let see what your network connection is doing on each PC, right click on network connection icon at lower right corner of your screen and select Connection Information to bring up the Connection Information screen. Below are screen shots for ethernet of my desktop and wifi of laptop connections respectively.
After reboot, call up Connection Information on each PC and make note of IP address of each. Open Terminal and type
$ ping -c 4 192.168.1.248 (replace 192.168.1.248 with actual IP address of the other PC)
If successful, you will get the output below showing success of ping:
PING 192.168.1.248 (192.168.1.248) 56(84) bytes of data.
64 bytes from 192.168.1.248: icmp_seq=1 ttl=64 time=208 ms
64 bytes from 192.168.1.248: icmp_seq=2 ttl=64 time=128 ms
64 bytes from 192.168.1.248: icmp_seq=3 ttl=64 time=48.6 ms
64 bytes from 192.168.1.248: icmp_seq=4 ttl=64 time=275 ms
--- 192.168.1.248 ping statistics ---
4 packets transmitted, 4 received, 0% packet loss, time 3004ms
rtt min/avg/max/mdev = 48.606/165.069/275.371/85.061 ms
Now try sharing folders. Could take a few minutes the first time sharing samba so have patience.
In the IPv4 section, the first 3 sets of number in the IP Address field should be the same (192.168.1 in this case) and the subnet mask should be identical. If this is not true, first thing to check is the connection setup. Right click on the network connection icon and select Edit Connections to bring up the Editing screen. Click on the IPv4 Settings tab and set Method to Automatic (DHCP) as per screen shot below. Repeat on other PC and reboot both.
Mint Mate 19.1. Main rig is HP 800G2 I5 6500 16GB ram, 120GB boot drive, 2x3TB, 1x4TB data drives. Oldest rig is Mate 18.3 on Dell D620 with 32bits core duo.