An external RF stage would be a bad idea. All that would do is overload you RF input circuitry. The S-240 seems to be sensitive to overload.
If you are really interested in making it all work again, you might was to get a copy of the
S-240 Manual. It's about half way down the page and it's only $14. There is no guarantee that it will include a schematic. However, if you get it working well and decide to sell it, having a manual could increase it's value.
At
this page there are a couple of YouTube videos on the S-240. I didn't go through them in detail but the owner of the videos may have a copy of the schematic he can send you.
Here are a couple of
reviews for the S-240. The reviews set the production date to 1967 to 1971 (ham license: 1965; graduated HS:1967), which is a bit older than you thought. While the radio is entry level, it does get a pretty good review. I find it interesting that the reviews warn against a antenna that is longer then 10 feet. But that's only an issue when using the BFO.
It took a little hunting around but I did find a
schematic for the S-240 at the
RadioMuseum.org. I uploaded it to my web site so I could share it with you. The schematic appears to be nice and clear and has lots of voltage test points. Make sure you use a high impedance volt meter (e.g. VTVM) There are two other pages available that include a parts list, layout, and alignment instructions, but you should be able to get them yourself and maybe they are included in the $14 manual.
Looking over the schematic a bit shows me that there is a 2-transistor preamp (Q1 & Q2) built in, but it is for FM only. The short wave circuitry bypasses the preamp and goes directly into the mixer (Q3). If this transistor was damaged, you wouldn't hear anything.
But this brings up a possibility. Clean all of the switching with contact cleaner. Over the years, there can be lots of oxidation on the band switch. The oxidation can cause quite a lot of signal loss. And, the S-240 has a pretty sizable band switch. I use some cleaner that I got at Radio Shack many years ago, but you should be able to find some on Amazon. Like this
WD-40 Specialist Contact Cleaner Spray. Someone my have a suggestion for an other type of cleaner.
Next, I would take a careful look at all the polarized capacitors (electrolytics). These capacitors tend to leak over time. The base of the electrolytic, where the leads come out, should be clean. If you see any type of buildup, replace it.
One thing you need to consider is the demise of short wave broadcasting. The short wave bands are not the same as they were in the 60s, 70s, and 80s. Most of the big signal short wave stations are gone. As a Novice ham our 40 Meter band allocations were shared with the international broadcast stations. So we had to operate alongside some pretty powerful stations, and not cause any interference. Things would get pretty crowded in the evening. But now, international broadcast stations are pretty scarce.
Overall, restoring a radio to like-new condition, takes a lot of work, time, and sometimes money. Good luck with your radio.