SpaceFM works but will need a extra dependency of
raid-dm-3.8.10-tinycore.tcz 
OFFTOPIC I have submitted firefox v 21 and it loads without any error
On the old alpha thread mention was made of libpng and animation.
I am assuming you mean animated gif?
if so, firefox 21 runs such test site was
http://en.wikipedia.org/wiki/File:Rotating_earth_%28large%29.gifMore tests later.
Is it appropriate to talk about grub menu using core and rootfs here?
inxi loads ok
inxi -F
Resuming in non X mode: xrandr not found. For package install advice run: inxi --recommends
System:    Host: box Kernel: 3.8.10-tinycore i686 (32 bit) 
           Desktop: N/A Distro: Core Linux
Machine:   System: ECS product: 945GCT-M2 version: 1.x
           Mobo: ECS model: 945GCT-M2 version: ECS
           Bios: American Megatrends version: 080012 date: 05/14/2008
CPU:       Dual core Pentium CPU E5200 (-MCP-) cache: 2048 KB flags: (lm sse sse2 sse3 ssse3) 
           Clock Speeds: 1: 1203.00 MHz 2: 1203.00 MHz
Graphics:  Card: nVidia G96 [GeForce 9500 GT] 
           X-Vendor: N/A driver: Resolution: N/A 
Audio:     Card: Intel N10/ICH 7 Family High Definition Audio Controller
Network:   Card: Realtek RTL-8139/8139C/8139C+ driver: 8139too 
           IF: eth0 state: unknown speed: 100 Mbps duplex: full mac: 00:21:97:76:2d:da
Drives:    HDD Total Size: 84.1GB (18.6% used) 1: id: /dev/sda model: WDC_WD800JD size: 80.0GB 
           2: USB id: /dev/sdb model: DataTraveler_2.0 size: 4.1GB 
Partition: ID: / size: 1.8G used: 15M (1%) fs: rootfs 
           ID: /home size: 48G used: 4.9G (11%) fs: ext3 
           ID: swap-1 size: 0.52GB used: 0.00GB (0%) fs: swap 
           ID: swap-2 size: 1.08GB used: 0.00GB (0%) fs: swap 
Sensors:   None detected - is lm-sensors installed and configured?
Info:      Processes: 148 Uptime: 0:12 Memory: 397.2/2024.7MB 
           Client: Shell inxi: 1.8.17 
Note I am running vesa here so can ignore xrandr for this test