Captain reported numerous systems malfunctions that required maintenance actions and speculated that the problems may be related to the aircraft returning from long-term storage.

Narrative

We had an engine exceedance on takeoff out of ZZZ. First flight of the day; full aircraft with a 27K Bump takeoff; no assumed temperature. The First Officer and I did not notice the exceedance during takeoff and climb-out because it happened at 648 feet and 188 knots airspeed. We took off from Runway XX and I was the pilot flying. The takeoff instructions were a turn to 340 after takeoff; which is why we did not notice the exceedance. We came to realize the exceedance even happened when we shut down the engines in ZZZ1 after we landed. We called Maintenance and told them about the red box around the N1 gauge for the number one engine. Maintenance pulled up the information in the FMS and the exceedance was noted in the archives. I made an AML (Aircraft Maintenance Logbook) entry and the exceedance was short in duration and about 10 - 15 degrees beyond the temperature limits. The inspection for the event was just a visible inspection of the front and rear of the aircraft engine. Message was cleared in the FMS. The synopsis provided starts at the gate and continues throughout the flight from engine start to engine shutdown. The First Officer did a walkaround preflight and noticed a bird strike above the Captain's forward window. We called Maintenance and had them inspect and make a logbook entry. This was the first flight of the day.The aircraft had an inoperative HUD (Heads-up Display) and previous write-ups for weather radar failures and refusals. The radio altimeter had previous anomalies as well. A few cabin write-ups were also listed. We started both engines and did a recall check; and had a FLT CNTL amber six pack light up. Looked on the overhead and the yaw damper clicked off. The preflight was done and the yaw damper was on before engine started. I reengaged the yaw damper and continued the after-start checklist and taxied out to the runway. The performance data required a 27K Bump takeoff. We rotated and made a right turn to 340 degrees off of Runway XX. When I turned right; the aircraft seemed to have a dead zone of about 1 - 2 inches in the roll mode. I mentioned it to the FO (First Officer) and asked him to fly it and see if he feels the same thing. He did in fact feel the same anomaly I was experiencing. I retrimmed the flight controls when the aircraft was transferred back to me. I asked him to pull up the hydraulic page and the System A quantity was at 62%. On the ground; both systems' percentage read high 80's to low 90's. I continued to hand-fly and engaged the autopilot in the mid 20's and verified all systems were normal; other than the 62% System A hydraulic pressure. All parameters for all systems were normal.At cruise; I disengaged the autopilot once again to verify if the dead zone was still there and was in fact [still there]. The aircraft was safe to fly; deemed by both pilots. The First Officer verified as well when I transferred controls once again. We continued to ZZZ1 after reengaging the autopilot. On the way out to ZZZ1 there was weather but we were south of the weather band. The weather radar had the amber weather FAIL message pop up about a half dozen times. On descent we experienced a radio altimeter amber RA message on the Captain's PFD (Primary Flight Display); while descending through 7;000 ft. It cleared about 6;000 ft. on the arrival into ZZZ1. We shot an ILS and I clicked the autopilot off early to feel the aircraft. Same dead zone in the right roll still present; about 1 inch input of right dead zone roll. I also had the First Officer pull up the hydraulic page after we configured the aircraft and a strange anomaly existed. The System A hydraulic quantity read high 80's and the right System B now read low 60's. Exactly opposite from what we had at cruise.We landed uneventfully and taxied to the gate. After we shut the engine down was when we noticed the engine exceedance. My guess is that we did not notice the exceedance on takeoff because I was focused on the right roll dead zoneon the yoke. I had asked Dispatch to relay a message to Maintenance in ZZZ1 that had Hydraulic System A may need servicing. I also used ACARS to send an arms code for the weather radar intermittent failures. Also; a couple of cabin write-ups. Maintenance met the aircraft and I explained every experience. The aircraft was taken out of service. The next day it was flying again as I looked in the app. Most items signed off; with the exception of the HUD and some minor cabin write-ups. I believe this aircraft sat in the desert for a while; which is why it was experiencing all the maintenance issues. [I suggest] a more thorough inspection of the older aircraft after a long sit in the desert.