That is how my E8285A was acting just before it got to the point that nothing at all happened when I pushed the power switch. Replacing all of the electrolytic capacitors and one tantalum capacitor on the main power supply board fixed it. About a year ago, sourcing the parts was a frustrating process. I manged to get them all from Digi-Key but had to settle for second or third choice on some due to stock status, and had to order one from a third party supplier through Digi-Key community with a separate shipping charge. I replaced both batteries while I had it open.
Paul
N1BUG