I appear to have very similar symptoms with an Intel E6750, which supports VT-x. Virtualisation is turned on in the BIOS, but machines still do not start. Do you suggest anything else to try?
root@node02:~# lscpu
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
CPU(s): 2
On-line CPU(s) list: 0,1
Thread(s) per core: 1
Core(s) per socket: 2
Socket(s): 1
NUMA node(s): 1
Vendor ID: GenuineIntel
CPU family: 6
Model: 15
Model name: Intel(R) Core(TM)2 Duo CPU E6750 @ 2.66GHz
Stepping: 11
CPU MHz: 2667.000
CPU max MHz: 2667.0000
CPU min MHz: 2000.0000
BogoMIPS: 5320.37
Virtualization: VT-x
L1d cache: 32K
L1i cache: 32K
L2 cache: 4096K
NUMA node0 CPU(s): 0,1
root@node02:~# pveversion -v
proxmox-ve: 4.1-32 (running kernel: 4.2.6-1-pve)
pve-manager: 4.1-4 (running version: 4.1-4/ccba54b0)
pve-kernel-4.2.6-1-pve: 4.2.6-32
lvm2: 2.02.116-pve2
corosync-pve: 2.3.5-2
libqb0: 0.17.2-1
pve-cluster: 4.0-30
qemu-server: 4.0-44
pve-firmware: 1.1-7
libpve-common-perl: 4.0-43
libpve-access-control: 4.0-11
libpve-storage-perl: 4.0-38
pve-libspice-server1: 0.12.5-2
vncterm: 1.2-1
pve-qemu-kvm: 2.4-20
pve-container: 1.0-37
pve-firewall: 2.0-15
pve-ha-manager: 1.0-16
ksm-control-daemon: 1.2-1
glusterfs-client: 3.5.2-2+deb8u1
lxc-pve: 1.1.5-5
lxcfs: 0.13-pve3
cgmanager: 0.39-pve1
criu: 1.6.0-1
zfsutils: 0.6.5-pve6~jessie
root@node02:~# cat /proc/cpuinfo | grep flags | uniq
flags : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx lm constant_tsc arch_perfmon pebs bts rep_good nopl aperfmperf pni dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm lahf_lm dtherm tpr_shadow vnmi flexpriority
root@node02:~# qm start 100
Running as unit 100.scope.
Could not access KVM kernel module: No such file or directory
failed to initialize KVM: No such file or directory
start failed: command '/usr/bin/systemd-run --scope --slice qemu --unit 100 -p 'KillMode=none' -p 'CPUShares=1000' /usr/bin/kvm -id 100 -chardev 'socket,id=qmp,path=/var/run/qemu-server/100.qmp,server,nowait' -mon 'chardev=qmp,mode=control' -vnc unix:/var/run/qemu-server/100.vnc,x509,password -pidfile /var/run/qemu-server/100.pid -daemonize -smbios 'type=1,uuid=5dde9fe9-092e-4153-b255-a5f1c10b641c' -name firewall -smp '2,sockets=1,cores=2,maxcpus=2' -nodefaults -boot 'menu=on,strict=on,reboot-timeout=1000' -vga cirrus -cpu kvm64,+lahf_lm,+sep,+kvm_pv_unhalt,+kvm_pv_eoi,enforce -m 512 -k en-us -device 'pci-bridge,id=pci.2,chassis_nr=2,bus=pci.0,addr=0x1f' -device 'pci-bridge,id=pci.1,chassis_nr=1,bus=pci.0,addr=0x1e' -device 'piix3-usb-uhci,id=uhci,bus=pci.0,addr=0x1.0x2' -device 'usb-tablet,id=tablet,bus=uhci.0,port=1' -device 'virtio-balloon-pci,id=balloon0,bus=pci.0,addr=0x3' -iscsi 'initiator-name=iqn.1993-08.org.debian:01:c6c4417560c1' -drive 'file=/var/lib/vz/template/iso/OPNsense-15.7.18-OpenSSL-cdrom-amd64.iso,if=none,id=drive-ide2,media=cdrom,aio=threads' -device 'ide-cd,bus=ide.1,unit=0,drive=drive-ide2,id=ide2,bootindex=200' -drive 'file=/mnt/pve/Disks/images/100/vm-100-disk-1.qcow2,if=none,id=drive-virtio0,format=qcow2,cache=none,aio=native,detect-zeroes=on' -device 'virtio-blk-pci,drive=drive-virtio0,id=virtio0,bus=pci.0,addr=0xa,bootindex=100' -netdev 'type=tap,id=net0,ifname=tap100i0,script=/var/lib/qemu-server/pve-bridge,downscript=/var/lib/qemu-server/pve-bridgedown,vhost=on' -device 'virtio-net-pci,mac=62:30:33:34:38:62,netdev=net0,bus=pci.0,addr=0x12,id=net0,bootindex=300' -netdev 'type=tap,id=net1,ifname=tap100i1,script=/var/lib/qemu-server/pve-bridge,downscript=/var/lib/qemu-server/pve-bridgedown,vhost=on' -device 'virtio-net-pci,mac=66:63:35:37:30:61,netdev=net1,bus=pci.0,addr=0x13,id=net1,bootindex=301'' failed: exit code 1