>Should I come to work early to make up for its power up/down time or should that be the company's responsibility - if they want me to work more or better should they provide better equipment? 

I had this situation before. "Hibernate" would consistently crash my machine so I had to shutdown/startup completely every day. I was also required to take my computer home at night, which meant I either had it crash or took 10+ min to startup.

This is even worse if you are salaried because you normally won't get any level of "compensation" for your time. You want to force this as an obvious problem. Likely your entire team is dealing with this...

**Don't give your personal time to account for company stupidity.** 

Some things you can do:

 - Have your bios start the machine automatically at a specific time, 15 min before you get to work
 - Start your computer manually before you get to work (or when you are traveling there)
 - Find other things to do during the startup time
 - Leave it on at work
 - Add this time as part of every time estimate you make (this will get attention)