You have spent $450 - $500 on a great radio and then you handicap the radio with a poor antenna system.
When you are on the very fringe of a radio system in the 700 - 800 range the signal is going to be weak so you need the best antenna system. So in your case I would do the following.
1. Buy a decent antenna. Multi-band antennas are not real good for 700-800 systems. Consider a Yagi pointed at the tower.
2. Buy decent coax like LMR400. Yes it is expensive but so is the radio.
3. Get rid of the splitter. It is eating up whatever little signal you are getting.
I have a similiar situation to yours and I use a Diamond J Discone with 50' of LMR400 for conventional frequencies running in to a duplexer and a Yagi 800 Mhz with 50' of LMR400 running into a Hamtronic amplifier and then into the duplexer and then the duplexer into the radio. Works beautifully. The amplifier on the end of the LMR picks up enough signal to give the signal enough boost to be able to hear a system that is 25 miles away.
Trust me I know, the antenna is something I would like to replace, it is an antenna I purchased about 5 years ago when I went with external antenna, but I do not have the money for that right now honestly. I only got the scanner now because I couldnt pass up the deal at $300. Also I listen to all bands, and do not want to get into multiple antennas with one scanner. I have though about modifying the Discone and adding in either two 3.5" elements at the bottom of the verticles, or adding a single 3.5" element halfway up the VHF element.
Dealing with just the cable and doing some math, this is what I have came up with.
I have a 25ft section of RG8 coming off the antenna going to the splitter, and then about 60 feet of RG6 to my scanner.
Specifically looking at the 770MHz (what I want to monitor that is so far away) I am looking at about 1.4dB loss on the RG8 (5.7 dB at 100 feet RG8) and then the splitter is another 3dB loss (from what I have read passive 1 in 2 out splitter) and then about 2.78dB loss on the RG6 (5.56dB/100feet) total of 7.18 dB loss.
If I remove the 25ft RG8 going up to the antenna and remove the splitter and reroute the RG6 to about a 45-50 ft run I would reduce my dB loss to 2.78dB total.
I never really got into the dB loss figures before, and never worked in signal transmission like this where it mattered, I just assumed I was too far away. The more I have read and figured out how systems work I have figured out more about it all.
So with my system in place the way it is. If I am receiving 50% of the original signal from the broadcast tower, and 3dB loss is 50% reduction, I figure I am getting less than 10% of the original signal strength at my scanner.
By doing what I want with removing the splitter and rerouting, etc I should be able to get 2.5x's that and receive 25% of the original signal strength at my scanner.
I hope my math and research is correct. And if it is, adding the 800mhz element would further increase my signal reception. (Though to be honest I do not understand why, I always though a piece of metal will pick up any signal, the wave lengths and need for different lengths for each band is something I dont get. Time for more research.)