As I understand it, more than likely you can go to the website and download the version of SketchUp for which you purchased the license and use the auth code given at the time of purchase to install it on your new machine.
Though your maintenance agreement has lapsed, it can be reinstated if you choose. If it was a recent lapse, you may still be within the grace period for reinstatement with no penalty fee. Even if a penalty is assessed, the cost is lower than purchasing a new license outright.
The following was excerpted from the SketchUp website at this url: Need to re-install, but maintenance has lapsed
What if my upgrade, maintenance, and support program expires?
It’s important to note that your SketchUp Pro license will always work for the version of Pro that you paid for. SketchUp Pro licenses will not stop working when your upgrade, maintenance, and support program expires. For example, if you purchased a new license for SketchUp Pro 2015 on December 1st, 2014, you would get a perpetual Pro 2015 license that would not expire. You would also get upgrades, maintenance, and support until November 30th, 2015 (i.e. one year after the purchase). If you would like to join the maintenance and support plan after your plan has expired for more than 30 days, there would be a $50 reinstatement fee, and you would start a new twelve-month support term.
To continually get the annual SketchUp Pro upgrades, maintenance, and support, year after year, you will need to renew the program again for $95 per year for single-user licenses and $150 per year per seat for network licenses. Don’t worry, we’ll let you know when you’re nearing the end of your program so that you have time to renew if you choose to do so.