I recently joined a gym thinking I'd have everything I needed to get a good workout. The problem is that I went to work out today, and found out that all the equipment I thought I'd have access to are reserved for people with personal trainers. So, all I have to work with now is:

a horizontal bench w/ barbell
a seated cable pulldown machine
a two sided cable machine w/ pull up bar and attachments
a few other barbells w/ weights
a few dumbbells, the heaviest being 35 lbs.
a college board
bouldering/climbing walls.

I'm used to working out at the rec. center at the nearby university which had every piece of equipment I could want. Now I'm not sure I'll be able to get in shape the way I want to in preparation for an upcoming police academy.

I have until November, so ideally I'd like to put on as much muscle as possible while increasing my strength as well as increasing my running ability from 3 miles to 10 miles.

Basically, my question is can I meet my fitness goals with the equipment listed in addition to running, sprinting, etc. outside of the gym?

Dude, that is messed up about the gym ... punks.

Anyway, you have everything you need easily. You could get in military/police shape with just the barbell .. trust me.

I would jump into a military style workout since that most closely reflects what you will see at the academy.

I suggest a deadlift and side-press routine M-W-F
Do Cals/abs then cardio T-TH-Sa
Stretch every day

Focus on pull ups, push ups, sit ups, running for the drills/tests at the academy. You will do yourself a great favor by trying HIIT with your cardio and cals. That way, when you get to the academy, you will smoke everyone else. Trust my experience on that one.

That is what I suggest for a normal young guy in average/above avg shape for mil/pol training. If you are quite overweight/very out of shape then I would do it a bit different.

Yeah. You could obviously use a few things, but that's still much more than some folks have. Either way, I'd look into 'unjoining' that gym out of principle.

Look at the Russian military. All they had was kettlebells, and they would destroy us in wrestling. Their power lifters were extremely strong as well. Just goes to show that if you have the will, you need little else.