First - there are two parts to the latching mechanism on the trunk - the actual latch in the sill, and the pull-down mechansim in the lid.

If the trunk closes and properly engages the latch in the sill, regardless of the condition of the pull-down mechanism, the trunk is CLOSED and will not open until the latch is released.

If your reversing aids don't pull down, and the doors don't lock, then the problem is with the PSE pump under the passenger rear seat. You should be able to hear the pump run when you lock/unlock the doors. If you don't, check the fuses. According to AllData, fuse 3 in the trunk controls the PSE pump, but I also see an entry for fuse 11. If you hear the pump but nothing is happening, there may be a leak. AllData references a problem where hoses come disconnected from the pump.

The PSE pump is only used in conjunction with the trunk close assist, and this is only to extend the pawl in the lid more quickly so the trunk can be opened and re-closed more rapidly. The PSE pump has no part in the "pull down" of the trunk lid when closed. If the PSE pump is out, then likely the pawl isn't extending, so closing the trunk will be more difficult, but it can be closed - try using a bit more force.

Check the doors to see if they still pull shut when closed to the first latch position.

The previous owner's records for my '97 S320 show two work orders for trunk closure problems. There are indentations in the top of the trunk lid. Clearly they were caused by closing the lid with hands on top of the trunk. They are very subtle, but I am going to investigate having them worked out by one of those dent remover folks.

So be careful how you place your hands when closing the trunk.

Steve