ReadyNAS 528x connect to 2 PCs

Each pc is directly connected to the NAS? If so, you need to use a different subnet for each connections.

1. Let's say your main subnet for all the machines is 192.168.0.0/24.

2. On the NICs to connect the first PC to the NAS, use 192.168.101.0/24 (or a /30). 

3. On the NICs to connect the second PC to the NAS, use 192.168.102.0/24 (or a /30).

You can't have two separate layer 2 networks connected to the same NAS on which you use a unique layer 3 addressing.

What else have you done?  If you have just plugged them in and expected it to work, i suspect that's the issue.  In the absense of a DHCP server or specific static IP address set,  each LAN port will adopt the default IP address.  While I've not tried that (because it's not how Ethernet is supposed to work), I doubt the NAS would handle both NIC's at the same address well.

The best way to do this is to have a router (not just a switch).  They cost way less than $500.  Amazon sells a NETGEAR WNR3500L for $39.99.  You can turn off the wifi if you like.  It's hard to find a home router without wifi these days.  But since you have internet access, doesn't your provider's equipment also include a router?  If you just run out of ports or are far from the router and don't want more long cables, then you do need a switch, like the NETGEAR GS305 at $18.20 on Amaon.

If you really want to connect them directly to the computers, you will have to go into the Network page of ReadyNASOS and open the settings for each NIC.  On the IPV4 tab, choose static and a private IP address.  Chose a different one for each.  You should probably also disable IPV6 on each.  Then you need to go into the network configuration on each computer and assign them an IP address in the same sub-net (same first 3 numbers) as the NAS port to which it is attached.

If you mess something up and lose connection with the NAS, an OS re-install will put it back to the original condition of  using DHCP and will also reset the admin password back to password.  Be careful not to do a factory default, as that also wipes you data.