01 EX: strange electrical problems

We got our '01 EX from its 1st owner in '03. Although new, the van had been in a couple of bad accidents with that owner. While the van was fixed fairly well, it seems that there was at least one problem that never got resolved. Over the years we took to a couple of shops but the problem could not be diagnosed.

The problem is electrical and occurs when it's cold -- like now. The symptoms occur in two very different places: the two automatic doors and windshield wipers.

The doors sometimes do not open, when controlled from the remote. They make clicking sounds but do not actually move. They still work when opened/closed using the buttons on the front panel. Similarly, sometimes they do not close when the handle on the door itself is pulled -- only when I use the front panel buttons. One door seems to be worse than the other.

The wipers do not move at first when I turn them on (intermittent or constant, does not matter). To get them to move, I have to turn them off and then on again, sometimes a couple of times.

What's going on here? Are these two problems related or totally separate? Are they easy/cheap to fix?

Thanks!