While there may not be a Sliders-based role playing adventure board game...there is a reasonable facsimile thereof.
Fringeworthy is a role playing adventure set in the year 2010 where a group of Japanese scientists discover a portal to a parallel existence and the united world intends to explore it. Much like the idea behind "Stargate," these portals are located on several parallel earths in a sort of chain...and only 100,000 people have that certain X-factor which allows them to use the portal. You are one of those lucky few.
An interesting feature of this RPG is that it has the ability to interconnect with some time travel RPGs (since parallel time lines and parallel earths are arguably one and the same). So, if you ever wanted the true Dungeons and Dragons experience with a Sliders taste; check out Fringeworthy. You can find a link to the Tri Tac Fringeworthy site (packed with info about the game) by clicking on the portal above.