There is no road to Silver Lake. There is a road to the Mayflower mine (elevation 11,000)but many people park at an obvious switchback at 10,600 because the next zig-zag causes palpitations. It is narrow and steep on loose rock. Going up looks better than going back down. However, lots of people do get to the Mayflower in a 4wheel. From the Mayflower there is a pack trail to Silver Lake (elevation 12,186). It is about 2 miles to the lake. But, there is likely to be a significant snow crossing on a steep couloir until mid-July or later. This crossing is just past the Mayflower so you can easily decide whether you want to cross it. I would not do so when there is snow there. Silver Lake is certainly worth the effort. So, come ahead and try. If there is snow stopping you at the Mayflower, there are lots of other great hikes in the area.
If you want to get to the other end of the tunnel mentioned in the last post, you go up into Dives Basin from Howardsville and Cunningham Gulch. Both ends of the tunnel are collapsed and sealed.