The hashes match, which means the file was correctly downloaded. Now open ImgBurn, switch to Verify mode, point ImgBurn to your ISO image and verify it against the burned disc.
Your problem has no relation to 32/64-bit architectures.
Here is the log file from imgBurn after verifying the ISO image against the burned disc.
I 20:41:29 ImgBurn Version 2.4.1.0 started!
I 20:41:29 Microsoft Windows XP Professional (5.1, Build 2600 : Service Pack 2)
I 20:41:29 Total Physical Memory: 2,096,624 KB - Available: 1,297,436 KB
I 20:41:30 Initialising SPTI...
I 20:41:30 Searching for SCSI / ATAPI devices...
I 20:41:40 Found 1 CD-ROM and 1 DVD