Sometimes the thought of changing something like that is much scarier than the actual doing...
Your DVD / Entertainment unit shares all the connectivity that a similar brand would have for the same functions. It will have power in, sound out for a minimum of one speaker group, most likely several speaker groups (inside, outside and a possible third that would be your choice or not used), antenna input, and video out. All the connections are reasonably standard and most new units come with a "How To" installation manual.
To find units that fit... The AWM960 has mounting hole dimensions of 9.3" across by 6.16" high (your hole is probably 9 1/4" wide by 6" high). A decent stereo shop can find replacements to fit that hole or you could contact a web oriented site like Crutchfield...
You may or may not have gotten the full Owner's Manual on your Jensen, if you didn't, you can download it here:
Jensen AWM960 Stereo/DVD Player
The manual gives you all the color codes for the various wires and what they go to...a new stereo would have the same type manual listing their wiring. Just match up the names
I understand, though, your reluctance. My father, rest his soul, was never certain which end of a screwdriver to hold and he always wondered where I got my mechanical ability from (he told me he suspected that the milkman may have been my father....
) Replacing the bad unit with another is defintely a lot easier; it will be plug and play. The only "unknown" or gamble is whether the new one will be better or worse than your existing unit