What
@GiGaBiTe said. Also, the two smaller ones are Y capacitors.
I only suggest changing those old film capacitors out because they're pretty much guaranteed to blow sooner or later.
Hopefully you have a component tester or even better an ESR/LCR in-circuit tester. In any event, what I would do is remove each of the capacitors (make sure to discharge them first if you've turned it on within the last 30 minutes) and test them. They may still be good. Then I would do as
@GiGaBiTe suggested and reflow the solder joints, especially where the cables plug in, the flyback transformer, and the voltage regulators. Basically anything that gets hot or experiences tension (or, preferably, just do the whole board just incase.) It's a time consuming process, but it needs to be done on these old boards.
Given how cheap capacitors are (for the ones that can be replaced), you could just replace them anyway instead of checking them. They may be fine, but also, it's relatively cheap for some preventative maintenance since you'll likely be desoldering them to test them anyway.