Trek bike tire not holding air?

Got this bike as a gift a few years ago (my dad won it in some contest). It's supposedly worth $1100. special addition canadian molson mountain bike (something like that).
anyway, the tires NEVER hold their air. i got a special adapter at a bike shop in colorado to air it up.
so, i thought maybe something is wrong w/ the inner tube...but there IS no inner tube.

i finally got the front tire to hold air--i didn't nkow i had to twist the little valve stem before putting the cap on.

but now, the back tire will not inflate at all. it's totally flat; i can hear air leaking out, but i can't find any holes anywhere. it's never been ridden, so the tires should be fine. the tire is not flush against the metal wheel...is that the problem? any help is appreciated--thanks.

that's "special edition"

As with most things related to bicycles, you can find info on different tire valve systems at sheldonbrown.com. If you have tubeless tires, you'll have to get the bead up against the rim all the way around before it'll start holding air. When I have that problem with tires on my lawn tractor, I run a rope around the outside circumference of the tire and cinch it tight, which pushes the beads out against the rim. A tire shop might be able to help if you can't get it.

It sounds like you have Presta valves. You need to loosen the metal top to fill the tire and then tighten it again when the tire is full. Then you put the cap on.

You need someone with a bit of experience to look at the bike to tell you what's going on with the tires. Almost every experienced rider I know will be glad to do this for you, for free, just because they love the sport. You can find these guys hanging around bike shops! Just ask.

HTH