Virtualbox supports your configuration (64-bit guest on 32-bit host), but there are some requirements and other caveats:
From the manual:
VirtualBox supports 64-bit guest operating systems, even on 32-bit host operating systems, provided that the following conditions are met:
You need a 64-bit processor with hardware virtualization support (see the section called “Hardware vs. software virtualization”).
You must enable hardware virtualization for the particular VM for which you want 64-bit support; software virtualization is not supported for 64-bit VMs.
If you want to use 64-bit guest support on a 32-bit host operating system, you must also select a 64-bit operating system for the particular VM. Since supporting 64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this support upon explicit request.
On any host, you should enable the I/O APIC for virtual machines that you intend to use in 64-bit mode. This is especially true for 64-bit Windows VMs. See the section called “"Advanced" tab”. In addition, for 64-bit Windows guests, you should make sure that the VM uses the Intel networking device, since there is no 64-bit driver support for the AMD PCNet card; see the section called “Virtual networking hardware”.
Please ensure you are meeting all these requirements, and that your memory allocation is reasonable -- try 512MB only for Backtrack to start with.
The other option is to try the free VMWare Player instead, which also supports this configuration, and see if it works any better.
Finally, even though you have 4GB RAM, if you can, you should just upgrade your physical machine to 64-bit 11.10 or 12.04. There should be no performance penalties with your configuration.