Make certain you are at BIOS rev A13, available here -> http://www.dell.com/support/drivers/us/en/19/DriverDetails/Product/inspiron-1564?driverId=R301036&fileId=2731118546&osCode=W764#OldVersion
Choose the File Name: "FLASHME_v103_Win_1194_4M_1564A13.exe" and select "download file", then "Single File Download" (FFS, don't use Dell's download manager!) You can run this BIOS upgrade directly from your desktop.
If you are already at that BIOS revision, then pull just one SODIMM module and replace it with an old 2GB module. If you have 6GB RAM, then you know the 4GB module you pulled is bad. If you have 2 GB of RAM, then you can guess that the still-installed-4GB module is bad. OR, you can just pull a 4GB module (leaving 4GB in) and boot. See if it posts to BIOS with 4GB. Then swap the 4GB SODIMMs and do it again, one of them should fail.