Thanks jmattson, your assumptions seem to be correct.
Increasing the memory of each ESX host to 6GB I was able to power on almost all of them, with the last four ones erroring out because of the limited swap space:
PowerCLI C:\Program Files (x86)\VMware\Infrastructure\vSphere PowerCLI> Get-Vm | Start-VM Name PowerState Num CPUs MemoryGB ---- ---------- -------- -------- TCLVM1 PoweredOn 1 0,063 TCLVM-68 PoweredOn 1 0,063 TCLVM-35 PoweredOn 1 0,063 TCLVM-36 PoweredOn 1 0,063 TCLVM-37 PoweredOn 1 0,063 TCLVM-38 PoweredOn 1 0,063 TCLVM-17 PoweredOn 1 0,063 TCLVM-39 PoweredOn 1 0,063 TCLVM-18 PoweredOn 1 0,063 TCLVM-15 PoweredOn 1 0,063 TCLVM-16 PoweredOn 1 0,063 TCLVM-19 PoweredOn 1 0,063 TCLVM-30 PoweredOn 1 0,063 TCLVM-31 PoweredOn 1 0,063 TCLVM-10 PoweredOn 1 0,063 TCLVM-32 PoweredOn 1 0,063 TCLVM-33 PoweredOn 1 0,063 TCLVM-91 PoweredOn 1 0,063 TCLVM-34 PoweredOn 1 0,063 TCLVM-13 PoweredOn 1 0,063 TCLVM-14 PoweredOn 1 0,063 TCLVM-92 PoweredOn 1 0,063 TCLVM-11 PoweredOn 1 0,063 TCLVM-72 PoweredOn 1 0,063 TCLVM-90 PoweredOn 1 0,063 TCLVM-12 PoweredOn 1 0,063 TCLVM-95 PoweredOn 1 0,063 TCLVM-73 PoweredOn 1 0,063 TCLVM-96 PoweredOn 1 0,063 TCLVM-74 PoweredOn 1 0,063 TCLVM-93 PoweredOn 1 0,063 TCLVM-75 PoweredOn 1 0,063 TCLVM-54 PoweredOn 1 0,063 TCLVM-94 PoweredOn 1 0,063 TCLVM-55 PoweredOn 1 0,063 TCLVM-99 PoweredOn 1 0,063 TCLVM-52 PoweredOn 1 0,063 TCLVM-53 PoweredOn 1 0,063 TCLVM-70 PoweredOn 1 0,063 TCLVM-71 PoweredOn 1 0,063 TCLVM-97 PoweredOn 1 0,063 TCLVM-50 PoweredOn 1 0,063 TCLVM-98 PoweredOn 1 0,063 TCLVM-51 PoweredOn 1 0,063 TCLVM-76 PoweredOn 1 0,063 TCLVM-77 PoweredOn 1 0,063 TCLVM-78 PoweredOn 1 0,063 TCLVM-58 PoweredOn 1 0,063 TCLVM-79 PoweredOn 1 0,063 TCLVM-59 PoweredOn 1 0,063 TCLVM-56 PoweredOn 1 0,063 TCLVM-57 PoweredOn 1 0,063 TCLVM-45 PoweredOn 1 0,063 TCLVM-44 PoweredOn 1 0,063 TCLVM-43 PoweredOn 1 0,063 TCLVM-26 PoweredOn 1 0,063 TCLVM-42 PoweredOn 1 0,063 TCLVM-25 PoweredOn 1 0,063 TCLVM-41 PoweredOn 1 0,063 TCLVM-40 PoweredOn 1 0,063 TCLVM-28 PoweredOn 1 0,063 TCLVM-27 PoweredOn 1 0,063 TCLVM-08 PoweredOn 1 0,063 TCLVM-07 PoweredOn 1 0,063 TCLVM-06 PoweredOn 1 0,063 TCLVM-29 PoweredOn 1 0,063 TCLVM-05 PoweredOn 1 0,063 TCLVM-49 PoweredOn 1 0,063 TCLVM-20 PoweredOn 1 0,063 TCLVM-48 PoweredOn 1 0,063 TCLVM-09 PoweredOn 1 0,063 TCLVM-47 PoweredOn 1 0,063 TCLVM-22 PoweredOn 1 0,063 TCLVM-46 PoweredOn 1 0,063 TCLVM-21 PoweredOn 1 0,063 TCLVM-24 PoweredOn 1 0,063 TCLVM-23 PoweredOn 1 0,063 TCLVM-82 PoweredOn 1 0,063 TCLVM-04 PoweredOn 1 0,063 TCLVM-81 PoweredOn 1 0,063 TCLVM-03 PoweredOn 1 0,063 TCLVM-80 PoweredOn 1 0,063 TCLVM-02 PoweredOn 1 0,063 TCLVM-01 PoweredOn 1 0,063 TCLVM-63 PoweredOn 1 0,063 TCLVM-86 PoweredOn 1 0,063 TCLVM-62 PoweredOn 1 0,063 TCLVM-85 PoweredOn 1 0,063 TCLVM-65 PoweredOn 1 0,063 TCLVM-84 PoweredOn 1 0,063 TCLVM-64 PoweredOn 1 0,063 TCLVM-83 PoweredOn 1 0,063 TCLVM-89 PoweredOn 1 0,063 TCLVM-61 PoweredOn 1 0,063 Start-VM : 01/06/2014 16:50:21 Start-VM The operation for the entity "TCLVM-88" failed with the following message: "Failed to extend swap file from 32768 KB to 103424 KB." At line:1 char:10 + Get-Vm | Start-VM + ~~~~~~~~ + CategoryInfo : NotSpecified: (:) [Start-VM], GenericVmConfigFault + FullyQualifiedErrorId : Client20_TaskServiceImpl_CheckServerSideTaskUpdates_OperationFailed,VMware.VimAutomation.ViCore.Cmdlets.Commands.StartVM TCLVM-60 PoweredOn 1 0,063 Start-VM : 01/06/2014 16:50:22 Start-VM The operation for the entity "TCLVM-87" failed with the following message: "Failed to extend swap file from 32768 KB to 103424 KB." At line:1 char:10 + Get-Vm | Start-VM + ~~~~~~~~ + CategoryInfo : NotSpecified: (:) [Start-VM], GenericVmConfigFault + FullyQualifiedErrorId : Client20_TaskServiceImpl_CheckServerSideTaskUpdates_OperationFailed,VMware.VimAutomation.ViCore.Cmdlets.Commands.StartVM Start-VM : 01/06/2014 16:50:22 Start-VM The operation for the entity "TCLVM-67" failed with the following message: "Failed to extend swap file from 32768 KB to 103424 KB." At line:1 char:10 + Get-Vm | Start-VM + ~~~~~~~~ + CategoryInfo : NotSpecified: (:) [Start-VM], GenericVmConfigFault + FullyQualifiedErrorId : Client20_TaskServiceImpl_CheckServerSideTaskUpdates_OperationFailed,VMware.VimAutomation.ViCore.Cmdlets.Commands.StartVM TCLVM-66 PoweredOn 1 0,063 Start-VM : 01/06/2014 16:50:22 Start-VM The operation for the entity "TCLVM-69" failed with the following message: "Failed to extend swap file from 32768 KB to 103424 KB." At line:1 char:10 + Get-Vm | Start-VM + ~~~~~~~~ + CategoryInfo : NotSpecified: (:) [Start-VM], GenericVmConfigFault + FullyQualifiedErrorId : Client20_TaskServiceImpl_CheckServerSideTaskUpdates_OperationFailed,VMware.VimAutomation.ViCore.Cmdlets.Commands.StartVM
I haven't checked out the contents of a running VM's directory because as I was approaching 100 running VMs things were starting to crash on my computer. I've increased the paging file to 6GB. I'll report back after a reboot.