Precision 470 takes 5-10 minutes to start boot process and turns itself off without warning (PSU issue?)

I have a Dell Precision 470 workstation. For several years it has been working fine. Now suddenly I am getting the following problems:

When turned on for the first time in the morning it takes 5-10 minutes before the BIOS info shows. Once the boot process has started however, it starts up normally. When the power is initially turned on, the LED behind the power button and the LEDs labelled A B C D on the front light up. However the screen is black for 5-10 mins until there is a click (like a relay) and the BIOS info appears.

Also, the PC turns itself off a couple of times in the first hour after being switched on. There is the click sound then the screen goes black. The LED behind the power button and the LEDs labelled A B C D on the front remain lit (although I think some go from green to yellow). Again it takes 5-10 minutes before the PC comes back on. This happens a couple of times, then generally it stays on without power loss for the rest of the day (although it does sometimes turn itself off at random times). When the shutdown happens there is no BSOD, and no event is recorded in the Windows event log.

There have been no hardware changes for several months prior to this problem occurring, and no changes made to the BIOS (firmware or settings). It seems to me like something in the power supply is "wearing out". Should I replace the whole PSU or do these symptoms indicate some other problem?

Many thanks.