I think I may have figured out your infrastructure: It sounds like you have a client PC with two NIC's in it, one NIC connected to you "main" network and another connected to a second network network that only hosts your NAS...
ISP<-->[WAN]router1{LAN]<--->[NIC1]PC[NIC2]<-->{LAN}router2[LAN]<-->NAS
The "main" network (LAN) is between router1 and your PC's NIC1 (and includes everything else connected to that network) and the "second" network (LAN) is between the PC's NIC2 and your NAS (and anything else connected to that network if there is anything.)
Such a configuration is fine, however you need to ensure there are no IP addressing conflicts for it to work properly.
In IP internetworking (with a small "i") each LAN on the network (called a subnet in IP jargon) must have a different and unique network address. (Incidentally the same is true on the public Internet (with a big"I."))
If both your routers have been obtained from the same ISP, then there's a very good chance they have both shipped using the same IP subnet address for their LAN's - very probably some form of 192.168.X.Y. That will cause problems as the routing in your PC will be screwed up.
The "fix" is pretty simple - you just need to change one of your routers to use a different IP subnet to the other. You could change either router, but it's probably simplest to change the one serving your NAS subnet as there's fewer devices connected to it and so doing will not affect anything on your main subnet.
Note the IP addressing of your "main" subnet - particularly what it's "X" is. Physically disconnect your PC from the main subnet (NIC1 as I've drawn it.) and let NIC2 and your NAS acquired IP addresses from router2 - you might need to reboot them to force a refresh.
Then navigate to the admin screen of router2 using it's LAN IP address - one reason for disconnecting NIC1 whilst we do this is to ensure you don't accidentally reach router1.
Once there, change router2's LAN IP address to a different subnet from that you noted earlier. IE, change the LAN IP address so that the "X" is different to the main subnet. It could be anything between 0-255, but it''s best to make it as "obvious" as possible.
As a worked example, IIRC BT ship their routers pre-configured to use 192168.1.Y. So the "NAS" subnet could be anything from 2-255, (technicaly you could also use 0,) so to pick a number out the air at random I'll choose 55. So router 2 gets it's LAN address changed to 192.168.55.1 (subnet mask 255.255.255.0.) So doing may (should) cause it to change it's DHCP range - but check it just the same. It may then need a reboot to take effect - indeed it's probably a good idea to reboot the router in any case.
Having effected the change, you need to force you NAS and PC (NIC2) to acquire new DHCP leases from the now changed router2 - so probably reboot them again (still disconnected from NIC1.) Once rebooted, check that they now have 192.168.55.Y IP addresses and check you can access your NAS.
Once that's all verified, plug PC NIC1 back in and everything should be sorted.
Alternatively, if both your PC and NAS have gigabit ethernet NIC's or 10/100 NIC's that can do something called auto-MDI/MDI-X (most do these days - it sorts out cable crossing automatically) you could dispense with router2 entirely and cable your NAS direct to your PC's NIC as
@ajohnson30 suggested previously. However, in such a configuration, as you now no longer have a DHCP Server on the "second" subnet you will have to manually configure both your NAS and PC (NIC2) with suitable IP addresses. That's easy peasy on a Windows PC, but if your NAS has no capacity to attach a screen and keyboard to "configure" things, you may not be able to manually set it up with (what "in the business" we call) a "static IP address.