Mac mini stuck on apple logo screen

Long story short, my booting problem disappeared immediately after upgrading my Mac mini (Mid 2011) to 4 GB of memory, from its original 2 GB, following this Apple article. The memory upgrade kit cost me about GBP 43.

I do not know if it was connected, but Verbose Mode had included this line in its log while the booting problem was being experienced:

kernel: (BootCache) BootCache: cache size (1388314624 bytes) too large for physical memory (0x80000000 bytes), capping at 0x40000000 bytes

Also, once booted via Verbose Mode, the Memory Pressure in Activity Monitor was often amber and sometimes red.

For completeness, the Boot ROM Version at the time of the original problem was MM51.007B.B00 and an extended AHT gave the same result as the short AHT: no hardware problems identified.

The performance of the upgraded Mac mini, once booted, is also much improved.

Thank you for your interest. My problem is this: I can boot up only via Verbose Mode (or Single-User Mode) (and that happens quickly, in a couple of minutes). In the case of all the following, my Mac mini boots to a grey screen with an Apple logo (no progress bar) and is stuck there, apparently indefinitely: normal restart/turn-on, Recovery Mode, Internet Recovery Mode (see #4 further below), Startup Manager, a bootable installer (see #5 further below), and a reinstall after erasing the hard drive (see #6 further below).

Conclusion: Given that the problem persists after a hard disk erase and reinstall (see #6), I have concluded that either: (1) likely, there is a bug in High Sierra 10.13.3: it is not compatible, in this regard (being able to boot normally), with my version of Mac mini (mid-2011); or (2) unlikely, my Mac mini has developed some hardware fault, not detectable by AHT, that causes High Sierra not to be able to boot normally but which did not prevent Sierra or previous versions of macOS from booting normally.

Updates and investigations:

1. Disk Utility/First Aid reported a problem with the drive, but not longer does so: In an earlier post, I said that First Aid reported no problems. That was (and still is) for the 'Macintosh HD' volume (the only volume listed). I did not realise then that I could run First Aid on the parent device itself (which is 'Toshiba MK5065GSXF Media'). First Aid on the drive reported that 'Problems were found with the partition map which might prevent booting'. That sounded like an accurate diagnosis, given my problems booting, but First Aid said it could not fix it and that First Aid needed to be re-run in Recovery Mode. Unfortunately, there seemed to be no way to reach Recovery Mode (see further below). More confusingly, re-running Disk Utility/First Aid on the drive now no longer reports a problem with the partition map and, in fact, reports no problems.

2. Apple Hardware Test (AHT): I can boot to the AHT (by holding down the D key after the turning-on chime). The short test passes. After the AHT I 'restart' and it boots to the grey screen with the Apple logo and nothing further happens. After the AHT, I remove one of my two screens (the HDMI one), so that there is only one screen attached (the DisplayPort one), in case that has any effect on what I am experiencing. It has no effect.

3. Recovery Mode: (Command + R) after a longer than usual pause, the plain grey screen changes to the grey screen with the Apple logo (no progress bar) and nothing further happens. (In respect of 'nothing further happens', I can tell from the small sounds the hard drive makes, the slight clicks and whirs, if it is reading or writing; 'nothing further' includes the hard drive apparently not doing anything either.)

4. Internet Recovery Mode: (Option + Command + R) this brings up a screen with a spinning globe and a progress bar. After about 5 minutes, the progress bar is complete. At this point the screen changes to the grey screen with an Apple logo (no progress bar) and nothing further happens (I have waited up to a few hours).

5. Bootable installer: I created a bootable installer for High Sierra following Apple's instructions here and using a brand new 32 GB USD 3.0 drive. The volume was not presented as an option in System Preferences/Startup Disk - which showed only 'Macintosh HD macOS, 10.13.3'. I didn't know why: none of the possible causes in this Apple article applied. However, this third-party article from 2014 implied that a USB drive needs to be reformatted with a partition scheme 'GUID Partition Table' to be bootable. (Despite 'createinstallmedia' reporting a step 'Making disk bootable...', it appears it does not, in fact, make bootable USB drives.) I did that, retraced my steps, and now the volume appears in Startup Disk.

In Startup Manager, the bootable USB drive appears as an option. Selecting it moves straight to the grey screen with an Apple logo (no progress bar) and nothing further seems to happen (I have waited over half an hour).

I set USD drive as the start-up disk in Startup Disk. It booted to the grey screen with the Apply logo (no progress bar) and nothing further seemed to happen. That takes me to step #6.

6. Erase hard drive and reinstall High Sierra: Although I cannot boot normally from the USD drive (in #5), I can boot from it in Verbose Mode. This brings up the 'macOS Utilities'. I used that to erase the 'Toshiba MK5065GSXF Media' device (including its apps and data) and then to reinstall High Sierra (following this Apple article). The clean install boots to the grey screen with the Apple logo (no progress bar) and nothing further seems to happen.

However, I try to reassign the hard drive as the start-up disk (using the Control key in Startup Manager, as in this Apple article). I can then boot up from the hard drive in Verbose Mode. That gets me to a black screen with a white Apple logo (with a progress bar) and a message that the Mac mini is 'installing'. When that progress bar is complete, the mini appears to restart and boots to the grey screen with the Apple logo (no progress bar) and nothing further seems to happen. However, I can power-off/power-on and boot into Verbose Mode and the installation continues to the setting-up of a 'new' Mac mini.

The 'fresh' Mac mini gets stuck on booting at the grey screen with the Apple logo, as before. However, it boots via Verbose Mode.

An update of the problem and a partial work-around: the Mac mini (mid 2011, not mid 2010 as I original thought; the memory is 2 x 1 GB) will not get past the grey 'Apple logo screen' (no progress bar) on any normal restart but will boot via Verbose Mode (Command + V after the turning-on chime sounds; or Windows + V, on a USB keyboard). I mentioned I had waited up to an hour stuck on the logo screen; I also waited overnight/for a working day. It now has High Sierra (v 10.13.3) and no outstanding updates (according to the App Store app). The disk is fine (according to Disk Utility/First Aid) with ~433 GB free of a 500 GB drive. Once booted, it seems to be fine (if slow but perhaps not as slow as before). I've not yet re-tried booting into Recovery to see if that is still broken.

Despite the work-around, any suggestions for a full fix would be gratefully received.