To be quite short - just sell them! For collectors some are quite valueable - and here's a list with some hidden gems just looking for a collector ==> Long list of albums for sale. If anyone looking at this wants to make an offer send me a comment! Or if you have information about maximising the value of this history.
The long story is a bit different. Of course it is possible to digitise the music on a PC. Take a simple twin output connector from an amplifier to the sound input socket on the standard feature that most PC have. And process the signal with Audacity or any one of many other recording programs which can encode the sound in a suitable format - MP3 or WAV or one of many others. Next you need to play through the music and identify the gaps between the tracks and split the album file into a series of files - one for each track. Then name each track. Then store using a music organising program and add the necessary data so that you can retrieve music by artist, album, track name, etc.
Having been through a similar exercise moving my LP music to minidisc I know how much time this takes - even before you consider how to illiminate pops and scratches. And based on my experience this is not a route for me.
There are a couple of companies in the UK who digitalise vinyl records as a service. The cheapest I found charges £14 per album. For several hundred albums this is very expensive, and anyway more expensive than buying CDs where the equivalent exists. http://shawsounds.net/lp_to_cd is one example, here is another http://www.audiorestored.com/.
There's a crossover point between cost and time which varies from person to person. But I'm not prepared to spend the hundreds of hours required to record my LP collection, so the only practical option is replace with CDs where possible and then digitising them on the PC.
Music download is another option - but the second-hand CD route seems the most economic - download prices are often more in line with new CDs.
So the answer to the question posed in this section is:-
1. Catalogue the vinyl and sell the collection.
2. Using the catalogue find replacement music on used CDs.
Amazon is a reasonable bet - prices go up and down depending on availability, but much music can be had for less than £4 including delivery. Stores specialising in second-hand records will sell CDs starting at around £3.00. They may also offers to purchase vinyl. My local shop sells most LPs for £1, so I expect the market is rather limited.
My record cabinet is still fully weighed down with my collection. When it is empty I will report back!