Thank you very much for all the answers.
For clarification:
A SOLUS USB stick provides the following information about the tower PC:
Hardware model - ASUS All Series
Memory - 16 GB
Processor - Intel Core IS 4440 x 4
Graphics - Intel HD Graphics 4600 (HSW GT2)
The BIOS settings are:
ASUS UEFI BIOS Utility - EZ mode
Q87M-E BIOS version 1103
CPU type: Intel Core i5-4440 CPU @ 3.10GHz
Memory 16384MB (DDR3 1600MHz)
BOOT
SecureBoot status - activated
Platform-Key (PK) Status - not loaded
Type of operating system - Other (Not Windows)
CMS (Compatibility Support Module) - enabled
-> Boot Device Control UEFI and Legacy OPROM
Boot Option Priority - UEFI OS
I am basically surprised by the following, I will name the 3 SSDs used 1 to 3 and describe what I have done with them:
SSD 1
This has Ubuntu Budgi - I can't remember which PC the version was installed on. In any case, it runs under the settings described above on the TowerPC.
The two SOLUS SSD discs are interesting:
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SSD 2
This was fitted with SOLUS on the ASUS notebook (about six months ago), updated and runs on both the notebook and the tower PC. I don't have to change anything in the BIOS (settings above).
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SSD 3
This was initially fitted with SOLUS on the tower PC, the installation stick was removed and the system did not run. At first I thought the disc was defective. So I repeated the installation on the notebook under the same conditions (same stick, same SSD). The version runs on the notebook without any problems. Conclusion: Installation medium OK, disc OK, system installation OK. Changing the SSD to the tower PC again leads to the sobering result that it does not boot. I've already ‘turned all sorts of screws’ in the BIOS (SecureBoot on and off, boot sequence of the disc shifted back and forth, UEFI AND Legacy - ONLY UEFI - ONLY Legacy mode set, ...). nothing helped).
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I am at my wit's end. I would be very interested to know what the problem is, an alternative is to install SOLUS on a stick and boot it, this works without any problems on the tower PC.
Maybe he just doesn't like SOLUS ... unlike me ;-)