[HTC Amaze 4G] zandgreen:
jdh2000:

There is a half of partitions that are missing on your partition table (no idea how they could have been screwed) and that's why the system can't mount them anymore.

Look, here is your partition table:

Device Boot Start End Blocks Id System
/dev/block/mmcblk0p1 * 1 17 128 4d Unknown
Partition 1 does not end on cylinder boundary
/dev/block/mmcblk0p2 17 49 256 51 Unknown
Partition 2 does not end on cylinder boundary
/dev/block/mmcblk0p3 49 4094 32367 5d Unknown
Partition 3 does not end on cylinder boundary
/dev/block/mmcblk0p4 4094 1923584 15355920 5 Extended
Partition 4 does not end on cylinder boundary
/dev/block/mmcblk0p5 4095 4096 16 5a Unknown
/dev/block/mmcblk0p6 4097 4129 256 73 Unknown
/dev/block/mmcblk0p7 4129 6684 20442+ 5b Unknown
/dev/block/mmcblk0p8 6684 6716 256 5c Unknown
/dev/block/mmcblk0p9 6716 6844 1024 45 Unknown
/dev/block/mmcblk0p10 6844 6876 256 47 Unknown
/dev/block/mmcblk0p11 6876 7132 2048 46 Unknown
/dev/block/mmcblk0p12 7132 7260 1024 4c Unknown
/dev/block/mmcblk0p13 7260 7264 32 39 Unknown
/dev/block/mmcblk0p14 7264 8032 6144 34 Unknown
/dev/block/mmcblk0p15 8032 8160 1024 36 Unknown
/dev/block/mmcblk0p16 8161 8192 256 76 Unknown
/dev/block/mmcblk0p17 8193 13313 40960 77 Unknown
/dev/block/mmcblk0p18 13313 18433 40960 77 Unknown
/dev/block/mmcblk0p19 18433 19457 8191 74 Unknown
/dev/block/mmcblk0p20 19457 20480 8190+ 74 Unknown
/dev/block/mmcblk0p21 20481 24576 32768 7a Unknown
/dev/block/mmcblk0p22 24577 26625 16384 48 Unknown
/dev/block/mmcblk0p23 26625 28672 16383 71 Unknown
/dev/block/mmcblk0p24 28673 30720 16381+ 76 Unknown
/dev/block/mmcblk0p25 30720 31232 4096 4a Unknown
/dev/block/mmcblk0p26 31232 31744 4096 4b Unknown

The first three primary partitions are fine:

/dev/block/mmcblk0p1

/dev/block/mmcblk0p2

/dev/block/mmcblk0p3

The extended partition is ok:

/dev/block/mmcblk0p4

But inside of the extended partition there are missing logical partitions (the missing part of the table I've taken from my fdisk output):

/dev/block/mmcblk0p27 31744 32256 4096 59 Unknown
/dev/block/mmcblk0p28 32257 32768 4096 5a Unknown
/dev/block/mmcblk0p29 32769 229376 1572863 83 Linux
/dev/block/mmcblk0p30 229377 270336 327679+ 83 Linux
/dev/block/mmcblk0p31 270337 598016 2621439+ 83 Linux
/dev/block/mmcblk0p32 598017 602078 32490 19 Unknown
/dev/block/mmcblk0p33 602078 602078 4 88 Unknown
/dev/block/mmcblk0p34 602078 602110 256 23 Unknown
/dev/block/mmcblk0p35 602110 602112 16 89 Unknown
/dev/block/mmcblk0p36 602113 1880064 10223616 c Win95 FAT32 (LBA)
/dev/block/mmcblk0p37 1880065 1880073 64 90 Unknown
/dev/block/mmcblk0p38 4095 4096 16 5a Unknown
/dev/block/mmcblk0p39 4097 4129 256 73 Unknown
/dev/block/mmcblk0p40 4129 6684 20442+ 5b Unknown
/dev/block/mmcblk0p41 6684 6716 256 5c Unknown
/dev/block/mmcblk0p42 6716 6844 1024 45 Unknown
/dev/block/mmcblk0p43 6844 6876 256 47 Unknown
/dev/block/mmcblk0p44 6876 7132 2048 46 Unknown
/dev/block/mmcblk0p45 7132 7260 1024 4c Unknown
/dev/block/mmcblk0p46 7260 7264 32 39 Unknown
/dev/block/mmcblk0p47 7264 8032 6144 34 Unknown
/dev/block/mmcblk0p48 8032 8160 1024 36 Unknown
/dev/block/mmcblk0p49 8161 8192 256 76 Unknown
/dev/block/mmcblk0p50 8193 13313 40960 77 Unknown
/dev/block/mmcblk0p51 13313 18433 40960 77 Unknown
/dev/block/mmcblk0p52 18433 19457 8191 74 Unknown
/dev/block/mmcblk0p53 19457 20480 8190+ 74 Unknown
/dev/block/mmcblk0p54 20481 24576 32768 7a Unknown
/dev/block/mmcblk0p55 24577 26625 16384 48 Unknown
/dev/block/mmcblk0p56 26625 28672 16383 71 Unknown
/dev/block/mmcblk0p57 28673 30720 16381+ 76 Unknown
/dev/block/mmcblk0p58 30720 31232 4096 4a Unknown
/dev/block/mmcblk0p59 31232 31744 4096 4b Unknown
/dev/block/mmcblk0p60 31744 32256 4096 59 Unknown

So, I think you can use 'parted' from 'adb shell' to add logical partitions (mmcblk0p[27-60]) to your extended partition (mmcblk0p4) using the data (start-end cylinder) from the table above.

Consider reading the parted manual first.

I hope it will be enough so that the system can use them again.