You initially said, "I have an issue routing between vlans".
Now you're saying "I cannot ping from one switch to the next even within the same vlan".
If you try to troubleshoot the Layer3 issue "I have an issue routing between vlans" when you have the Layer2 issue "I cannot ping from one switch to the next even within the same vlan", you won't get anything fixed.
Ignore Layer3 and inter-VLAN routing and address the Layer2 issue first.
I'd remove all those IP addresses from the switches - they will only confuse matters.
I'd delete all the trunks and LACP config.
Start off by patching the 2530 into one of the 3500s.
Configure the interfaces at both ends of the connection as "VLAN1 untagged" with no other VLANs on it.
Now put a host on a "VLAN1 untagged" interface on each of the two switches, give each of those hosts an IP address in the VLAN1 subnet and get them to ping each other.
Only after the above is working, add VLAN120 as a tagged VLAN to the interfaces on either side of the link between the 2530 and the 3500, change both the hosts' switch interfaces to "VLAN120 untagged" and get them to ping each other.
If you have that working, then you've got your VLAN trunking working OK, you can now create your distributed trunk, then repeat both tests to ensure VLAN1 and VLAN120 are still connected between the 2530 and the 3500s.
Only then, configure the trunk to the router with both VLANs 1 and 120 on it, either both tagged or 1 untagged, depending on the router config.
Cconfigure one of the hosts' switchports to VLAN1 untagged and get it to ping its default GW.
Reconfigure the IP address on the other host to an IP address that is in the VLAN120 subnet (leaving it on a VLAN120 untagged switchport) and get it to ping its default GW.
If both can ping their default GW, they will be able to ping each other. Job done.