The virtual machine has an (actually, potentially any number of) associated virtual disk(s), each of which in turn is one or more (generally very large) file(s) which, taken together, correspond to the "physical" hard disks that the operating system installed inside the VM sees.
Just like you can move a physical hard disk from one computer to another, you can attach a virtual hard disk to more than one VM, to copy files to and from it. In principle you can attach a single virtual disk to multiple VMs that are running simultaneously, but in practice it's a bad idea to run more than one VM at a time that uses a single virtual disk.
Since I don't have VMware in front of me, I can't tell you which menu options to pick, but it's there in the virtual machine properties somewhere. Look for IDE and SATA mappings; those will almost certainly name the disk file's location. Just copy that as a secondary disk into the other VM's settings, make sure the old VM is shut down, and start the new one. If you are lucky, the disk will show up without any further effort on your part and you can just copy files to and from it.
If it doesn't show up immediately, look in Windows' Disk Manager in the new VM after you have attached the disk to it, to see if the partition needs to be assigned a drive letter (sometimes it doesn't happen automatically, particularly if something broke). Also note that you will probably need to be logged in as administrator to be able to access the files.
The above assumes that you weren't running file-system-level or full-disk encryption on the old VM. If you were, you need to try to repair the old VM to get your files out.