My son has Office 2010 on his now DEAD laptop. 
So my question is, can we install Office again on another PC? Will the key still work?

So my question is, can we install Office again on another PC? Will the key still work?
My Computer
At a glance
W7 Prof 64 biti7-3770kG.Skill Sniper 1866 16 GBEvga GTX 770
- Computer type
- PC/Desktop
- Computer Manufacturer/Model Number
- HomieJunker
- OS
- W7 Prof 64 bit
- CPU
- i7-3770k
- Motherboard
- Sabertooth Z77
- Memory
- G.Skill Sniper 1866 16 GB
- Graphics Card(s)
- Evga GTX 770
- Sound Card
- Sound Blaster Z
- Monitor(s) Displays
- Asus VG278HE
- Screen Resolution
- 1920 x 1080
- Hard Drives
- 4 Seagate Barracudas 250 GB
2 Intel® X25-M 160GB
- PSU
- Corsair H1000X
- Case
- Lian-Li A77B
- Cooling
- Phantek 120 dual fans
- Keyboard
- Corsair K70 RGB
- Mouse
- Logitech G502
- Internet Speed
- FiOS Quantum
- Antivirus
- Avira
- Browser
- Chrome