I have recently configured a Dell PowerConnect 5524 with 3 VLANs (Dell PowerConnect 5524 VLAN routing).
I have connected this switch to our network with an IP of 192.168.2.254, it successfully routes traffic from the 192.168.3.0/24 subnet and even gets ping replies from our main router (the ASA on 192.168.2.1 and my PC 192.168.2.41) however if I try from my PC to ping anything on the other subnet, including the Dell's .3 IP (192.168.3.2), I get nothing.
I have added this route on the ASA:
route inside 192.168.3.0 255.255.255.0 192.168.2.254
This doesn't seem to work.
If I add the route on my PC itself (via route add in the command prompt) everything works fine.
The ASA and the Dell are directly connected via cable from port 21 on the Dell (VLAN 2, Internal .2) to port 5 on the ASA (VLAN 1, INSIDE).
If I change the default gateway in Windows on my PC to the IP address of the Dell on this subnet (192.168.2.254), I can access devices on the other subnet with no problems.
Full config for the PowerConnect can be found here.
Full config for the ASA (IPs and sensitive info has been blanked out) can be found here.
Best Answer
I would recommend using the switch as the default gateway for all of your subnets. For your scenario the default gateway of hosts on Vlan 3 should be set to 192.168.3.2 and hosts on Vlan 2 should be set to 192.168.2.254.