Well, first- almost any exercise can be modified to make it harder as you get more fit. If you run or bike or do any cardio- go faster or longer. The same principle can be applied to strength training. If doing 10 pushups is a challenge now, do that. When that becomes easier, work on doing 15 pushups, and then keep adding reps. This can be applied to any body weight exercise- pushups, crunches, lunges, squats, rows, bench presses, chest flys, bicep curls, whatever- without access to barbells (though some you will need dumbbells at least!)
As for getting your HR up- why not go out?! If you can, go for walks and runs outside. The sun will do you good too
If for whatever reason that isn't an option (but don't be making excuses!), try jump rope or a workout DVD. You might not be ready for INSANITY, but you could try some Kathy Smith aerobics- a little dated but fun nonetheless. Jumping jacks, tae bo, running in place, dancing- you have a lot more options than you might think.