Note: Sent this as an answer to the PM, which I admittedly rarely check. Thought it might be of benefit in the thread:
Hi Dave... apologies on a tardy reply. We were spending a few nights at the Poulsbo marina, and I generally try to go 'off grid' when boating. 😀
Although I can't truly rule anything out at this point, I highly doubt that the addition of the accumulator is cause of your issue. Mostly because the hot side is delivering decent water pressure/volume, right? Both hot and cold water lines benefit from the accumulator, so what happens to one side will happen to the other as well. Pressure balancing spools generally let all cold water go directly through the valve mostly unimpeded. What they do is use the pressure from the cold line to actuate the hot going through the cartridge. When the cold pressure drops, the spool slides to one side and diminishes the hot volume as well, which helps keep one from getting scalded. Note that it doesn't 'stop' the hot water... but depending on brand, it just slows it down a little. The cold water does pass through the spool, so if debris got stuck in the spool, it could choke the cold water only, whilst letting full hot pass by.
ITC is generally an RV/Marine valve which is rarely used in residential plumbing (which is where my expertise lies), so I don't have a good parts breakdown at my disposal. I'm sure you'll be able to find one online, however.
Within this valve is not only the main mixer cartridge, which houses a pressure balancing spool, but on either side of the main cylinder should also be integral stop valves, which are simply flat-blade screwdriver stops. One on each side, cold and hot. If you were to remove the large escutcheon (typically removed by removing the handle (allen set screw, mainly) and 2 screws), you will see these stops on either side of the main center cylinder if your valve has these (optional, but common).
The first thing I would check is to see if the cold side screwdriver stop is all the way open. Could be as simple as that! However, they don't close on their own, so unless the valve has been serviced recently, it's unlikely it's closed. However, debris can wedge itself in this valve's body and create this issue, so it's probably a good idea to remove the integral screwdriver stop stem to check. The screwdriver slotted stem sits within a bonnet which is hex, so you can remove the bonnet and stem with a deep socket.
I would check there first. In addition, if you have someone handy, you can use a bucket and have someone turn on the pump after the stop stem has been removed to see how good the flow is at that point. I have a feeling that it will spray out heartily, so be prepared to have them shut the pump off quickly. Also, I like to put some tinfoil under the opening so no water makes its way into the wall cavity...
If the flow is good there, then it's definitely the main cartridge. If the cold just dribbles out of the open hole where the integral stop stem was... there's a problem somewhere between the pump and that shower valve. Unlikely though... If that's the case, let me know and we can discuss options.
If, once you remove the stop stem, you find debris... just clean out what you can (typically, using the flushing method above will do the trick) and put the stop back together to see if that solved the problem.
If the flow is good and there's debris in the cartridge, you might be able to remove the cartridge as I mentioned in the post and find debris that you can remove or flush out. Try that and replace the cartridge and test for flow.
If you don't see debris in the cartridge, then it's probably stuck within the pressure balancing spool, which is rarely accessible without breaking the cartridge. Thus, the need for a new cartridge.
You mention 'replacing the valve'? If it's just a debris issue, which is the most likely case, then replacing the entire valve (inside the wall) is not necessary. With the main cartridge and screwdriver stops removed, what's left in the wall is just a valve body, which rarely goes bad. So no need to replace. Unless the cartridge is problematic to find... which is unlikely though, as ITC uses (or used at one point anyway) knockoffs of large companies like Delta, Moen, and Price Pfister. In most cases, replacing the cartridge with their main company's OEM is better than OEM ITC parts.
I hope this all makes sense. Let me know how it goes! Also, I would think it beneficial for this info to be in the main thread for all to benefit... IF any of this works! :mrgreen:
Good luck!
Brian