This is pretty easy; hung parliament in 1992 means coalition between the Lib Dems and Labour - a generous PR system is implemented, but this creates splits in Labour and the coalition on that side becomes shaky. Kinnock, exhausated and demoralised, retires in 1994 and Blair is elected leader in his place, however the party is polarised and Blair begins to rely more and more on the Lib Dems. Labour formally splits in 1996, with the vast majority of the party and MPs disassociating themselves from Blair and the government; Blair is forced to call a general election after losing a confidence motion in 1996.
The Tories, under Norman Lamont, are having post-Thatcher troubles of their own, however, and when the general election comes, the LDs, under the reformed electoral system, emerge as the largest party, but without a majority of any substance. Ashdown begins forming his government.
Blah. Something like that.