What's wrong with my Honda???

Hi!
I have a 1994 Honda Civic hatchback. My mechanic says it is dual carburetor.
It has done roughly 135,000kms.
Recently it has been having a lot of trouble starting, mostly on cold frosty/wet mornings.
When it's frosty it's completely dead, no signs of life at all until it warms up later on in the day.
When it's wet it's like it's trying to turn over but it can't. We eventually got it started after 45mins of revving and pumping the gas like mad.
In both of the above situations, after it is started it cuts out very easily, especially when taking off/slowing down to a stop when revs are low. It seems to rev very low for a long time and takes a very long time to warm up properly. It also cuts out if I have the heater on as this seems to affect the revs too.
I took it my mechanic and they told me I had a broken radiator and water pump so they fixed that but it hasn't changed anything, if anything it has gotten worse since then.
Let me know if you need any more info.
Thanks!
Sez.