I dont know if they are clogged but the amount of tree needles in the gutter i'm sure its clogged then. Best trick/device to unclog? Unfortunately there is a concrete walkway at the corner where it goes into the ground. Maybe my shop vac and a long hose.
A ********* ABS pipe is what you would typically have for a drain pipe. So your good there. If your downspout isn't connected to it, then once you fix this problem you'll want to get another piece of pipe or an extension to connect them better and have less spillage or debris getting inside. Best defense is a downspout screen at the top of your drain pipe inside the gutters. Sure, it'll eventually clog like everything else over time but it's a defense that you'll be able to clear out in seconds. It should easily stay clear between gutter cleanings or better part of the year - depending on your surrounding trees. I suggest using the plastic ones, metal rots quickly. Pic below.
Actual photos would be great. I'm with four.cycle. Havin a hard time picturing things. So it's hard to help effectively. For evergreen needles, a plumbing snake with the corkscrew end is most effective becasue those needles tend to weave themselves together im a jam, and that corkscrew will pul them apart and break it up quickly.
Best I can tell, it sounds like you have a plug somewhere. Those kind of pipes clog over time. All that dirt, debris etc etc goes down that pipe and low flow will allow it settle. As mentioned, gutters first, then remove that downspout pipe first along side of your house, check for a clog. If that clever tank vac trick doesn't work (in wet mode, not dry BTW), can you get ahold of a drain snake to clear it at either end? Be careful as those black ABS pipes can be brittle at the elbows and bends. Take your time, go slow. it'll be messy but keep water flowing while you do it.
On the cheap end, you could use brass hose jet cone end with the water on full blast and a small cone nozzle, snaking it down your pipe. I'd suggest lightly taping around the thread connector to smooth our any edges that might get hung up on anything - makes life easier. In a pinch I've had great success with that, but this could also compact a clog if not done carefully and gently. If you can, start at the end destination first - where the water ends up.
Critters do like those pipes as underground pre-dug tunnels. Rats and chipmunk squirrels will sometimes nest in them. Once you get it unclogged (if that's the issue) maybe place a drain screen over the pipe end? I've had chipmunks nest inside of my fence post pipes that didn't have the top dome caps on them. Crazy lil' buggerz!