Thank you Luke for providing a lot of initial info, but please provide some critical missing bits ...
What is your flow rate? This is really important to know.
You stated that your method is isocratic. What is the NORMAL system back-pressure you observe with this method (in psi or bars)?
Which detector are you using (and what are the exact settings) ?
Can you show us a chromatogram with the noise showing the scales?
There are many reasons for pressure to fluctuate and we really would need to be on-site to properly troubleshoot it. However, it could be something simple as you need to replace the PTFE frit inside the Prime/purge valve (this should be replaced every 1-month. Yes, every month). As it starts to clog up, all kinds of pressure problems start to happen. You also may have a mixing problem too (you mentioned that peaks change retention time which happens when either the flow rate is NOT what you think it is OR the mobile phase composition changes). Failure to properly flush and prime the system before use can also cause these problems too (and it should never take 16-hours to do this! More like 10-20 minutes at most). Yes, the degasser may be broken (and no, you probably will not see any error messages for this as they usually appear YEARS after the degasser is broken) as they last at most 3-years in the 1260 Quat and Binary pumps (very short lifetimes). When the integrated degasser is broken, the pump's performance will be poor in some cases, but it will also be adding debris into the HPLC system flow path resulting in pump instability, ghost peaks, and all kinds of other problems. One or more clogged solvent pickup filters can also lead to "pump problems" too so be sure and install new glass filters on the solvent bottle lines. If your pump is from Agilent's "value line" (IOW: No AIV), then it may have a contaminated passive inlet valve. When these valves start to 'stick', the pump will cavitate and become unstable with different solvent mixtures (clean the valve. NOTE: If your pump has the active inlet valve, leave it alone OR change the internal filter in the valve, but only have this done by an experienced tech).
BTW: Which Agilent Quat pump do you have? Please share the model number (found on the front label, it starts with 'G ####).
Here is a related article from our professional training classes. You may find it helpful, but please contact a professional chromatographer for assistance.
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Diagnosing & Troubleshooting HPLC Pressure Fluctuation Problems (Unstable Baseline)";
https://hplctips.blogspot.com/2014/01/d ... -hplc.html