Suddenly the black then blue log in screen appears. This has happened when Firefox was open, but I think it's possible that it happened when other programmes are on the screen.

Below is the ixni-Fx read out.

moshe@moshe-NC:~ > inxi -Fx
System: Host: moshe-NC Kernel: 3.13.0-24-generic x86_64 (64 bit, gcc: 4.8.2)
Desktop: KDE 4.13.1 (Qt 4.8.6) Distro: Linux Mint 17 Qiana
Machine: Mobo: ASUSTeK model: P5G41C-M LX version: Rev X.0x Bios: American Megatrends version: 0402 date: 01/21/2010
CPU: Dual core Pentium CPU E5800 (-MCP-) cache: 2048 KB flags: (lm nx sse sse2 sse3 ssse3 vmx) bmips: 12799.8
Clock Speeds: 1: 1203.00 MHz 2: 1203.00 MHz
Graphics: Card: Intel 4 Series Chipset Integrated Graphics Controller bus-ID: 00:02.0
X.Org: 1.15.1 drivers: intel (unloaded: fbdev,vesa) Resolution: 1680x1050@59.9hz
GLX Renderer: Mesa DRI Intel G41 GLX Version: 2.1 Mesa 10.1.3 Direct Rendering: Yes
Audio: Card-1: Intel NM10/ICH7 Family High Definition Audio Controller driver: snd_hda_intel bus-ID: 00:1b.0
Card-2: Logitech QuickCam IM driver: USB Audio usb-ID: 046d:08a6
Sound: Advanced Linux Sound Architecture ver: k3.13.0-24-generic
Network: Card: Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller
driver: r8169 ver: 2.3LK-NAPI port: d800 bus-ID: 01:00.0
IF: eth0 state: up speed: 100 Mbps duplex: full mac: 48:5b:39:a0:54:ad
Drives: HDD Total Size: 1303.2GB (39.1% used) 1: id: /dev/sda model: Maxtor_6L120P0 size: 122.9GB
2: id: /dev/sdb model: Hitachi_HDS72105 size: 500.1GB 3: id: /dev/sdc model: SAMSUNG_HM641JI size: 640.1GB
4: USB id: /dev/sdd model: DK23FB size: 40.0GB
Partition: ID: / size: 57G used: 21G (38%) fs: ext4 ID: swap-1 size: 7.30GB used: 0.03GB (0%) fs: swap
RAID: No RAID devices detected - /proc/mdstat and md_mod kernel raid module present
Sensors: System Temperatures: cpu: 36.0C mobo: 35.0C
Fan Speeds (in rpm): cpu: 2220 sys-1: 0
Info: Processes: 200 Uptime: 37 min Memory: 2782.2/3918.8MB Runlevel: 2 Gcc sys: 4.8.2 Client: Shell inxi: 1.8.4
moshe@moshe-NC:~ >

If I understand correctly, what you describe sounds as if KDE has crashed and thrown you out back to the display manager. I've had this happen with E17 on Magiea, even when the computer was unattended.

You might nose about in the Mint logs, which are located in /var/log, but I'm not familiar enough with Mint's log file structure to suggest which one, as there is no /var/log/messages file. I might start with Xorg.0.log, mintsystem.log, and syslog.

When I had the experience with E17, I found an error message in some Mageia log or other I forget which indicating that E17 was loosing its connection to X. I have been using KDE on that box for a test and the problem has not occurred with KDE--yet.